- Converting Fractions to Decimals
- Home
- Writing a Decimal and a Fraction for a Shaded Region
- Converting a Fraction With a Denominator of 10 or 100 to a Decimal
- Converting a Fraction With a Denominator of 100 or 1000 to a Decimal
- Converting a Proper Fraction With a Denominator of 2, 4, or 5 to a Decimal
- Converting a Mixed Number With a Denominator of 2, 4, or 5 to a Decimal
- Converting a Fraction to a Terminating Decimal - Basic
- Converting a Fraction to a Terminating Decimal - Advanced
- Converting a Fraction to a Repeating Decimal - Basic
- Converting a Fraction to a Repeating Decimal - Advanced
- Using a Calculator to Convert a Fraction to a Rounded Decimal
- Converting a Mixed Number to a Terminating Decimal - Basic
- Converting a Mixed Number to a Terminating Decimal - Advanced
- Ordering Fractions and Decimals

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# Converting a Fraction With a Denominator of 10 or 100 to a Decimal

We should recall decimal place value charts. We know that, to the right of a decimal, the places values are the tenths, hundredths, thousandths and so on.

*The rule says that the decimal point in the numerator shifts to the left as many places as the number of zeros after 1 in the denominator.*

Consider here, fractions with denominators of 10 or 100

**Rules to convert a fraction with a denominator of 10 to a decimal**

Suppose we have a fraction $\frac{7}{10}$.

At first, we write the numerator 7 only.

Then we look at the denominator which is a ten which corresponds to the decimal place value tenth. So, 7 has a place value of a tenth. For this we put a decimal point before 7. So, $\frac{7}{10}$ becomes the decimal .7 or 0.7

Alternately, as the number of zeros in a 10 is 1, the decimal shifts one place to the left in 7 to make it 0.7

**Rules to convert a fraction with a denominator of 100 to a decimal**

Next consider a fraction $\frac{97}{100}$.

At first, we write the numerator 97 only.

As we were dividing with a 100, we are looking at a place value of a hundredth. The digit 7 has a place value of a hundredth. So, a decimal point is put before 9 and we get $\frac{97}{100} = .97$ or $0.97$.

Alternately, as the number of zeros in a 100 is 2, the decimal point shifts two places to the left in 97 to make it 0.97

Write $\frac{6}{10}$ as a Decimal.

### Solution

**Step 1:**

At first, we only write the numerator 6 as 6.0

**Step 2:**

Since the denominator 10 has a single zero, we shift the decimal point in 6.0 one place to the left and get .6 or 0.6 as the answer.

**Step 3:**

So, $\frac{6}{10} = 0.6$

Write $\frac{48}{100}$ as a decimal.

### Solution

**Step 1:**

At first, we write the numerator 48 as a decimal 48.0.

**Step 2:**

Since the denominator 100 has two zeros, we shift the decimal point in 48.0 two places to the left, and get the answer as .48 or 0.48

**Step 3:**

So, $\frac{48}{100} = 0.48$