 # Convert tenths and hundredths between simplified fractions and decimals

Lesson

## Place value and decimals

In the same way that we can use the place value system to work out the value of a whole number, we can also think of fractions the same way.  This helps us to express a fraction as a decimal. To the right of our decimal point, we have tenths and hundredths.  So, $\frac{1}{10}$110 could be expressed as $1$1 in the tenths place, so our decimal would be written as $0.1$0.1. Likewise, $\frac{1}{100}$1100 means we have $1$1 in the hundredths place, which can be expressed in decimals as $0.01$0.01.

### Tenths to decimals

When our fraction is expressed as tenths, we need to write this with the number that appears on the top of the fraction, the numerator, in the tenths position of our decimal.  Here, in our first video, we look at how to express fractions, such as $\frac{4}{10}$410 as a decimal.

### Hundredths to decimals

In our second video, we look at fractions such as $\frac{35}{100}$35100, and express them as a decimal. The value of our number doesn't change, it's just that we write it in a different format.

You also see how a number like $60$60 hundredths might also be expressed as 6 tenths, or $0.6$0.6.

#### Examples

##### Question 1

Write the decimal $0.05$0.05 as a fraction in its simplest form.

##### QUESTION 2

Write the mixed number $5\frac{9}{25}$5925 as a decimal.

##### QUESTION 3

Write the decimal $1.65$1.65 as an improper fraction in its simplest form.

### Outcomes

#### NA4-6

Know the relative size and place value structure of positive and negative integers and decimals to three places.