This question tests 4th grade understanding of decimal notation for fractions with denominators 10 or 100, converting between forms and locating on number lines (CCSS.4.NF.6). Decimals are just another way to write fractions that have denominators of 10 or 100. The decimal 0.a (one digit after the decimal point) represents a/10 (a tenths), and the decimal 0.ab (two digits) represents ab/100 (ab hundredths). The decimal point separates the whole number part from the fractional part, with the place values to the right representing tenths, hundredths, etc. For fraction to decimal, 65/100 has denominator 100, so write 65 in the hundredths places: 65/100 = 0.65. Choice B is correct because 0.65 represents 6 tenths and 5 hundredths, totaling 65/100, and connects to money as 65 cents. Choice A adds an extra zero, making 0.065 or 65/1000, often from place value confusion. Teach using money: 65/100 dollar = $0.65; shade 65 squares on a grid; use charts to place digits in tenths and hundredths columns.

This question tests 4th grade understanding of decimal notation for fractions with denominators 10 or 100, converting between forms and locating on number lines (CCSS.4.NF.6). Decimals are just another way to write fractions that have denominators of 10 or 100. The decimal 0.a (one digit after the decimal point) represents a/10 (a tenths), and the decimal 0.ab (two digits) represents ab/100 (ab hundredths). The decimal point separates the whole number part from the fractional part, with the place values to the right representing tenths, hundredths, etc. For fraction to decimal: The fraction 45/100 has denominator 100, so write 45 in the hundredths places: 45/100 = 0.45. Choice A is correct because for 45/100, the 4 goes in tenths place and 5 in hundredths place, giving 0.45, demonstrating understanding that decimals and fractions are equivalent representations. Choice B represents decimal point placement error (adding an extra zero, making it thousandths), which happens when students don't understand place value determines fraction denomination. To help students: For fraction to decimal, denominator tells place value—45/100 means 45 in hundredths places = 0.45. Use hundredths grid: shade 45 squares, see 0.45; practice with place value chart and watch for wrong decimal point placement.

This question tests 4th grade understanding of decimal notation for fractions with denominators 10 or 100, converting between forms and locating on number lines (CCSS.4.NF.6). Decimals are just another way to write fractions that have denominators of 10 or 100. The decimal 0.a (one digit after the decimal point) represents a/10 (a tenths), and the decimal 0.ab (two digits) represents ab/100 (ab hundredths). The decimal point separates the whole number part from the fractional part, with the place values to the right representing tenths, hundredths, etc. For decimal to fraction: The decimal 0.9 has one decimal place, so the denominator is 10. The digit 9 after the decimal point becomes the numerator: 0.9 = 9/10. Choice A is correct because it matches the one decimal place with denominator 10. Choice C represents a wrong denominator (used 100 instead of 10), which happens when students confuse tenths and hundredths places. To help students: Count decimal places—one place = tenths (denominator 10). For 0.9: '9' in tenths place, so 9/10. Practice equivalence: 0.9 = 9/10 = 90/100. Use hundredths grid: shade 90 squares for 0.90 to show equivalence.

This question tests 4th grade understanding of decimal notation for fractions with denominators 10 or 100, converting between forms and locating on number lines (CCSS.4.NF.6). Decimals are just another way to write fractions that have denominators of 10 or 100. The decimal 0.a (one digit after the decimal point) represents a/10 (a tenths), and the decimal 0.ab (two digits) represents ab/100 (ab hundredths). The decimal point separates the whole number part from the fractional part, with the place values to the right representing tenths, hundredths, etc. For decimal to fraction: The decimal 0.5 has one decimal place, so the denominator is 10; the digit 5 after the decimal point becomes the numerator: 0.5 = 5/10. Choice B is correct because for 0.5, the 5 is in tenths place (5/10), demonstrating understanding that decimals and fractions are equivalent representations. Choice A represents wrong denominator (used 100 instead of 10), which happens when students don't count decimal places correctly. To help students: Count decimal places to determine denominator—one place = tenths (denominator 10); for 0.5: '5' in tenths place, so 5/10. Practice equivalence: 0.5 = 5/10 = 50/100; use money: $0.50 = 50/100 = 5/10 dollar.

This question tests 4th grade understanding of decimal notation for fractions with denominators 10 or 100, converting between forms and locating on number lines (CCSS.4.NF.6). Decimals are just another way to write fractions that have denominators of 10 or 100. The decimal $0.a$ (one digit after the decimal point) represents $a/10$ (a tenths), and the decimal $0.ab$ (two digits) represents $ab/100$ (ab hundredths). The decimal point separates the whole number part from the fractional part, with the place values to the right representing tenths, hundredths, etc. For grid to decimal: 29 shaded out of 100 represents $29/100$, which is $0.29$ in decimal form. Choice B is correct because $29/100$ means 2 in tenths place and 9 in hundredths place, giving $0.29$, demonstrating understanding that decimals and fractions are equivalent representations. Choice A represents decimal point placement error (adding an extra zero, making it thousandths), which happens when students misread digits or don't understand place value. To help students: Use hundredths grid: 100 squares, shade appropriate number, see connection between shaded count and decimal; for 29 shaded: $0.29$. Practice with place value chart: show digits in correct columns; watch for wrong denominator or confusing tenths and hundredths.

This question tests 4th grade understanding of decimal notation for fractions with denominators 10 or 100, converting between forms and locating on number lines (CCSS.4.NF.6). Decimals are just another way to write fractions that have denominators of 10 or 100. The decimal 0.a (one digit after the decimal point) represents a/10 (a tenths), and the decimal 0.ab (two digits) represents ab/100 (ab hundredths). The decimal point separates the whole number part from the fractional part, with the place values to the right representing tenths, hundredths, etc. For a hundredths grid with 47 squares shaded out of 100, the shading represents 47/100, which is the decimal 0.47. Choice A is correct because the 47 shaded squares out of 100 directly translate to 0.47, demonstrating understanding that decimals and fractions are equivalent representations. Choice B represents a wrong number of decimal places, like adding an extra zero, which happens when students miscount the shaded squares or confuse hundredths with thousandths. To help students: Count decimal places to determine denominator—one place = tenths (denominator 10), two places = hundredths (denominator 100). Use hundredths grid: 100 squares, shade appropriate number, see connection between shaded count and decimal. Practice equivalence: 0.47 = 47/100. Money connection: $0.47 = 47 cents = 47/100 dollar helps make concrete.

This question tests 4th grade understanding of decimal notation for fractions with denominators 10 or 100, converting between forms and locating on number lines (CCSS.4.NF.6). Decimals are just another way to write fractions that have denominators of 10 or 100. The decimal 0.a (one digit after the decimal point) represents a/10 (a tenths), and the decimal 0.ab (two digits) represents ab/100 (ab hundredths). The decimal point separates the whole number part from the fractional part, with the place values to the right representing tenths, hundredths, etc. For decimal to fraction, 0.90 has two decimal places, so denominator 100, with digits 90 as numerator: 0.90 = 90/100. Choice C is correct because it uses the full digits after the decimal over 100, showing equivalence including the trailing zero. Choice A simplifies to 9/10 but ignores the specified denominator 100, a distractor for not following instructions. To help, note that 0.90 = 0.9 but for denominator 100 it's 90/100; use equivalents 90/100 = 9/10; practice with charts emphasizing trailing zeros don't change value but affect fraction form.

This question tests 4th grade understanding of decimal notation for fractions with denominators 10 or 100, converting between forms and locating on number lines (CCSS.4.NF.6). Decimals are just another way to write fractions that have denominators of 10 or 100. The decimal 0.a (one digit after the decimal point) represents a/10 (a tenths), and the decimal 0.ab (two digits) represents ab/100 (ab hundredths). The decimal point separates the whole number part from the fractional part, with the place values to the right representing tenths, hundredths, etc. For fraction to decimal: The fraction 7/10 has denominator 10, so write 7 in the tenths place: 7/10 = 0.7. Choice B is correct because the 7 goes in the tenths place, giving 0.7, demonstrating understanding that decimals and fractions are equivalent representations. Choice A represents a wrong denominator confusion, like treating it as hundredths, which happens when students confuse tenths and hundredths places. To help students: Denominator tells place value—7/10 means 7 in tenths place = 0.7. Use place value chart: show digits in correct columns. Practice equivalence: 0.7 = 7/10 = 70/100. Watch for: decimal point in wrong place, not understanding place value determines fraction denomination.

This question tests 4th grade understanding of decimal notation for fractions with denominators 10 or 100, converting between forms and locating on number lines (CCSS.4.NF.6). Decimals are just another way to write fractions that have denominators of 10 or 100. The decimal 0.a (one digit after the decimal point) represents a/10 (a tenths), and the decimal 0.ab (two digits) represents ab/100 (ab hundredths). The decimal point separates the whole number part from the fractional part, with the place values to the right representing tenths, hundredths, etc. For locating on a number line: 0.62 is between 0.6 and 0.7, specifically at the second hundredth mark after 0.6. Choice B is correct because for 0.62, the 6 is in tenths place (6/10) and 2 is in hundredths place (2/100), located at correct position on number line representing 0.62. Choice A represents a wrong number line location, like swapping digits, which happens when students misread digits. To help students: Use number line marked in tenths and hundredths to plot points. Practice equivalence: 0.62 = 62/100, count 6 tenths and 2 hundredths from 0. Watch for: confusing tenths and hundredths, wrong placement.

This question tests 4th grade understanding of decimal notation for fractions with denominators 10 or 100, converting between forms and locating on number lines (CCSS.4.NF.6). Decimals are just another way to write fractions that have denominators of 10 or 100. The decimal 0.a (one digit after the decimal point) represents a/10 (a tenths), and the decimal 0.ab (two digits) represents ab/100 (ab hundredths). The decimal point separates the whole number part from the fractional part, with the place values to the right representing tenths, hundredths, etc. For the shaded grid, 47 out of 100 squares shaded means the fraction is 47/100, which converts to the decimal 0.47 by placing 47 in the hundredths places. Choice A is correct because 0.47 accurately represents 47/100, with 4 in the tenths place and 7 in the hundredths place, demonstrating equivalence between the shaded portion and the decimal form. Choice B represents a common error of adding an extra zero, making it 0.407 which is 407/1000 instead of 47/100, often due to misunderstanding place values. To help students, use a hundredths grid and shade 47 squares to visually connect to 0.47; practice counting shaded squares over total to form the fraction and then convert by noting two decimal places for hundredths.