$$0.8 = \frac{8}{10} = \frac{80}{100}$$ and $$\frac{15}{100}$$ is already expressed with denominator 100. To have the same denominator, both fractions need denominator 100. Choice A has different denominators (10 and 100). Choice C incorrectly converts 0.8 to $$\frac{8}{100}$$. Choice D creates an improper fraction $$\frac{80}{10}$$ and incorrectly converts $$\frac{15}{100}$$ to $$\frac{15}{10}$$.

When comparing fractions and decimals, you need to convert them all to the same form to see which values are actually larger or smaller.

Let's convert everything to decimals to make comparison easier. First, $$\frac{7}{10}$$ equals $$0.7$$ (since 7 divided by 10 is 0.7). Next, $$\frac{70}{100}$$ equals $$0.70$$ (since 70 divided by 100 is 0.70). We already have $$0.07$$ as a decimal.

Now we can easily compare: $$0.07$$, $$0.7$$, and $$0.70$$. Remember that $$0.7$$ and $$0.70$$ are exactly the same value - adding a zero after the last decimal place doesn't change the number's value. So we're really comparing $$0.07$$ and $$0.7$$.

Since $$0.07$$ means 7 hundredths and $$0.7$$ means 7 tenths (or 70 hundredths), $$0.07$$ is much smaller. From shortest to longest: $$0.07$$ meters, then $$\frac{7}{10}$$ meters and $$\frac{70}{100}$$ meters (which are equal).

Choice A incorrectly puts the two equivalent values in different positions. Choice B incorrectly places $$\frac{70}{100}$$ between the other two values, when it's actually equal to $$\frac{7}{10}$$. Choice D reverses the entire order, putting the largest values first.

The correct answer is C: $$0.07$$ meters, $$\frac{7}{10}$$ meters, $$\frac{70}{100}$$ meters.

Study tip: When comparing fractions and decimals, convert everything to the same form first. Also remember that equivalent fractions like $$\frac{7}{10}$$ and $$\frac{70}{100}$$ represent the same value.

When you need to convert a decimal to a fraction, think about place value. Each decimal place has a specific value: the first digit after the decimal point is tenths, the second digit is hundredths, the third would be thousandths, and so on.

For the decimal $$0.56$$, you have 5 in the tenths place and 6 in the hundredths place. Since the decimal goes to the hundredths place (two digits after the decimal), you write it as $$\frac{56}{100}$$. The numerator 56 represents the total number of hundredths in the decimal - literally fifty-six hundredths.

Looking at the wrong answers: Choice A has the correct fraction $$\frac{56}{100}$$ but incorrectly describes the numerator as "fifty-six tenths." This is wrong because 56 represents hundredths, not tenths. Choice B shows the decimal broken into parts ($$\frac{5}{10} + \frac{6}{100}$$), which is mathematically correct but doesn't answer the question about writing it as a single fraction. Choice C has the wrong denominator - $$\frac{56}{10}$$ would equal 5.6, not 0.56. It also incorrectly calls the numerator "fifty-six hundredths" when using tenths as the denominator.

The correct answer is D because it properly converts $$0.56$$ to $$\frac{56}{100}$$ and correctly identifies that 56 represents fifty-six hundredths.

Remember: when converting decimals to fractions, the denominator comes from the rightmost decimal place, and the numerator represents how many of those units you have in total.

$$\frac{73}{100} = 0.73$$ because 73 hundredths equals 0.73. Maria wrote 0.073, which represents $$\frac{73}{1000}$$ or 73 thousandths. To correct this, she needs to move the decimal point one place to the right. Choice B moves it the wrong direction. Choice C moves it too far. Choice D is incorrect because 0.073 ≠ $$\frac{73}{100}$$.

When you need to convert a decimal to a fraction, you're essentially translating between two ways of expressing the same value. The decimal $$0.05$$ means "5 hundredths," so you need to think about what that means as a fraction with 100 in the denominator.

To convert $$0.05$$ to a fraction with denominator 100, remember that the decimal already tells you the story. The digit 5 is in the hundredths place, which means you have 5 out of 100 equal parts. This gives you $$\frac{5}{100}$$ centimeters. The fraction $$\frac{5}{100}$$ literally means "5 out of 100 equal parts of a centimeter," so if you imagine dividing one centimeter into 100 tiny equal pieces, the leaf's thickness equals 5 of those pieces.

Choice A incorrectly explains what $$\frac{5}{100}$$ means by saying it represents "5 out of 10 equal parts." This confuses hundredths with tenths - $$\frac{5}{100}$$ is definitely about 100 parts, not 10.

Choice B converts the decimal incorrectly to $$\frac{50}{100}$$, which would equal $$0.50$$ (or $$0.5$$), not $$0.05$$. This is ten times too large.

Choice D uses $$\frac{0.5}{100}$$ in the numerator, but fractions should have whole numbers in both numerator and denominator when possible. Also, this would equal $$0.005$$, which is too small.

Study tip: When converting decimals to fractions, the place value tells you the denominator. Hundredths place means the denominator is 100, and the digits tell you the numerator.

When you see decimals written as fractions, remember that different fractions can represent the same value — these are called equivalent fractions. The key is understanding that $$0.3$$ and $$0.30$$ are exactly the same decimal, just written differently.

Let's prove that $$\frac{3}{10}$$ and $$\frac{30}{100}$$ are equivalent. You can multiply both the numerator and denominator of $$\frac{3}{10}$$ by 10: $$\frac{3 \times 10}{10 \times 10} = \frac{30}{100}$$. Since we multiplied by $$\frac{10}{10} = 1$$, we didn't change the fraction's value. You can also verify this by dividing: $$\frac{3}{10} = 0.3$$ and $$\frac{30}{100} = 0.30 = 0.3$$.

Answer A is wrong because just having different numerators and denominators doesn't make fractions different in value — only appearance. Answer B makes a false claim that all fractions with different denominators are equivalent, which isn't true (like $$\frac{1}{2}$$ and $$\frac{1}{3}$$). Answer C incorrectly states the fractions represent different amounts when they actually represent exactly the same amount.

Answer D is correct because $$\frac{3}{10}$$ and $$\frac{30}{100}$$ both equal $$0.3$$, making them equivalent fractions despite looking different.

Study tip: When comparing fractions or decimals, convert them to the same form (all decimals or all fractions with the same denominator) to see if they're truly equivalent. Don't be fooled by different appearances — focus on the actual values!

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 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 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.