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Fraction ↔ Decimal Workshop

Convert benchmark fractions into decimals and back using 100-square visual grids and place-value multipliers.

Step 1: The Briefing

Fractions and Decimals: Two Ways to Show the Same Amount

Imagine cutting a chocolate bar right down the middle with a friend. As a fraction, you have \(\frac{1}{2}\). On a calculator, kitchen scale, or price tag, that exact same half is written as \(0.5\). They look different, but they show the exact same amount!

Fraction Form: \(\frac{1}{2}\) of a whole Decimal Form: 0.5
1/2 = 0.50 (50%)
Fraction Form: \(\frac{3}{4}\) of a whole Decimal Form: 0.75
3/4 = 0.75 (75%)

Our decimal numbers count in groups of 10 and 100. If we divide one whole unit into a 100-square grid:

To turn a fraction like \(\frac{3}{4}\) into a decimal, we find an equivalent fraction with 100 on the bottom. Multiply numerator and denominator by 25:

\(\frac{3}{4} = \frac{3 \times 25}{4 \times 25} = \frac{75}{100} = 0.75\)  ↔  \(0.6 = \frac{6}{10} = \frac{3}{5}\)
Step 2: The Lab Bench

100-Square Grid Explorer

Adjust the slider or click benchmark presets to see how fractions, decimals, and hundredths line up on the grid.

Live Equivalences

Every hundredth represents one filled square out of 100.

Decimal Value 0.50
Fractional Equivalent 12 = 50100
Percentage 50%

100-Square Grid

Shaded hundredths

50 of 100 equal squares shaded (0.50 of the whole unit).

Step 3: Sparring Ring

Benchmark Readiness Check

Why does multiplying both parts of \(\frac{2}{5}\) by \(\frac{2}{2}\) convert it directly into a decimal?

Question 1 Completed: 0

Your Conversion Challenge

Start with step 1. Take your time—there is no timer.

No timer, sign-in, or penalties. Work through each step at your own pace to earn 25 XP per challenge.

Step-by-step lesson

Fractions and decimals: two ways to describe one quantity

Before you start: Understand equal parts, decimal tenths and multiplication.

Read the hundred-square grid

If the full grid represents 1, each of its 100 equal squares is 1/100 = 0.01. Thirty-five filled squares represent 35/100 = 0.35. A row of 10 squares is 10/100 = 1/10 = 0.1. The value of the whole must stay fixed while you compare representations.

Convert a fraction using an equivalent denominator

For 3/4, multiply numerator and denominator by 25: 3/4 = 75/100 = 0.75. This works because 25/25 = 1. The grid would show 75 filled squares. A percent means “per hundred,” so the same quantity is 75%.

Convert a decimal and simplify

The last digit of 0.45 is in the hundredths place, so 0.45 = 45/100. Divide both parts by their common factor 5 to get 9/20. Check: 9 × 5 = 45 and 20 × 5 = 100. Writing 45/10 would mean 4.5, ten times too large.

What if hundredths are not enough?

A fraction bar also means division. For 3/8, calculate 3 ÷ 8 = 0.375. That is 375 thousandths, so a grid of only 100 whole squares cannot display it exactly without splitting some squares. For 1/3, division repeats: 0.333… . The finite decimal 0.33 is an approximation, not exactly 1/3.

For a fraction in simplest form, the decimal terminates only when the denominator's prime factors are all 2s or 5s. Powers of 10 contain only those primes. Denominator 8 = 2³ allows thousandths; denominator 3 cannot be scaled to a power of 10 using an integer multiplier.

Try it yourself

Convert 7/20 to a decimal and percent. Is 0.35 the same quantity as 0.350?

Show answer and explanation

7/20 = 35/100 = 0.35 = 35%. Also 0.350 = 350/1000 = 35/100, so the trailing zero does not change the value.

Use the activity to check your understanding

Match a filled area with its fraction, decimal and percent. Explain whether a displayed decimal is exact or rounded.

Try the next activity: Decimal Number Line →

Sources and further reading