# Which proportion is shaded (in decimals)?

Decimals and fractions (easy)

## Fractions and decimals

Decimal numbers are another way to represent numbers that are smaller than the unit 1. Decimals are written to the right of the units place separated by a period called decimal point. The first digit to the right of the decimal point represents tenths, the second represents hundredths, the third represents thousandths, etc.

If you want to compare or do calculations with fractions and decimals, you need to convert all of them to one type (either decimals or fractions).

### Convert decimals to fractions:

**1. Convert the decimal to fraction** using tenths, hundredths, thousandths, etc. depending on the number of decimal places. 1 place=tenth, e.g. $0.5=5/10\; ; 3.3=33/10$, two places=hundredths, e.g. $0.02=2/100 \;; 0.12=12/100 \;; 1.38=138/100$,
three places=thousandth, e.g. $0.002=2/1000\; ; 0.304=304/1000$.

**2. Simplify the fraction to the lowest common term**, e.g. $5/10=1/2 \;; 2/100 = 1/50$.

### Convert fractions to decimals

**1. Find a number you can multiply by the denominator (bottom of the fraction) to make it 10, or 100, or 1000**, etc.

E.g.:

**2. A fraction in this form can be converted to a decimal**- just put the decimal point in the correct position (one space from the right hand side for every zero in the bottom number):

E.g. $5/10=0.5\;$ ; $25/100=0.25$

For some numbers there is no way to multiply them to become tens, hundreds or thousands. For these numbers you can calculate an approximate decimal (finding a denominator close to 10, 100 or 1000), e.g.:

### Convert whole numbers to fractions

Just put 1 below the whole number, e.g.:

Decimals and fractions (medium)

## Fractions and decimals

Decimal numbers are another way to represent numbers that are smaller than the unit 1. Decimals are written to the right of the units place separated by a period called decimal point. The first digit to the right of the decimal point represents tenths, the second represents hundredths, the third represents thousandths, etc.

If you want to compare or do calculations with fractions and decimals, you need to convert all of them to one type (either decimals or fractions).

### Convert decimals to fractions:

**1. Convert the decimal to fraction** using tenths, hundredths, thousandths, etc. depending on the number of decimal places. 1 place=tenth, e.g. $0.5=5/10\; ; 3.3=33/10$, two places=hundredths, e.g. $0.02=2/100 \;; 0.12=12/100 \;; 1.38=138/100$,
three places=thousandth, e.g. $0.002=2/1000\; ; 0.304=304/1000$.

**2. Simplify the fraction to the lowest common term**, e.g. $5/10=1/2 \;; 2/100 = 1/50$.

### Convert fractions to decimals

**1. Find a number you can multiply by the denominator (bottom of the fraction) to make it 10, or 100, or 1000**, etc.

E.g.:

**2. A fraction in this form can be converted to a decimal**- just put the decimal point in the correct position (one space from the right hand side for every zero in the bottom number):

E.g. $5/10=0.5\;$ ; $25/100=0.25$

For some numbers there is no way to multiply them to become tens, hundreds or thousands. For these numbers you can calculate an approximate decimal (finding a denominator close to 10, 100 or 1000), e.g.:

### Convert whole numbers to fractions

Just put 1 below the whole number, e.g.:

Compare decimals, fractions and whole numbers

## Fractions and decimals

Decimal numbers are another way to represent numbers that are smaller than the unit 1. Decimals are written to the right of the units place separated by a period called decimal point. The first digit to the right of the decimal point represents tenths, the second represents hundredths, the third represents thousandths, etc.

If you want to compare or do calculations with fractions and decimals, you need to convert all of them to one type (either decimals or fractions).

### Convert decimals to fractions:

**1. Convert the decimal to fraction** using tenths, hundredths, thousandths, etc. depending on the number of decimal places. 1 place=tenth, e.g. $0.5=5/10\; ; 3.3=33/10$, two places=hundredths, e.g. $0.02=2/100 \;; 0.12=12/100 \;; 1.38=138/100$,
three places=thousandth, e.g. $0.002=2/1000\; ; 0.304=304/1000$.

**2. Simplify the fraction to the lowest common term**, e.g. $5/10=1/2 \;; 2/100 = 1/50$.

### Convert fractions to decimals

**1. Find a number you can multiply by the denominator (bottom of the fraction) to make it 10, or 100, or 1000**, etc.

E.g.:

**2. A fraction in this form can be converted to a decimal**- just put the decimal point in the correct position (one space from the right hand side for every zero in the bottom number):

E.g. $5/10=0.5\;$ ; $25/100=0.25$

For some numbers there is no way to multiply them to become tens, hundreds or thousands. For these numbers you can calculate an approximate decimal (finding a denominator close to 10, 100 or 1000), e.g.:

### Convert whole numbers to fractions

Just put 1 below the whole number, e.g.:

Dividing decimals

## Multiplying and dividing decimals

We can multiply decimal numbers just as if they were whole numbers (ignore the decimal point and divide it with 10, 100 or 1000 based on the number of decimal places). Afterwards we put the decimal point into its proper location in the result - it will move as many decimal places as the original numbers combined, e.g.:

You can also convert decimals to fractions, e.g.:

Converting repeating decimals to fractions

## Repeating decimals

A **recurring/repeating decimal** is a number whose digits are periodic (repeating its values at regular intervals) and keep repeating forever, e.g. $1/3=0.333333 ...$ The infinitely repeated digit sequence is called the **repetend**. It can be denoted by a horizontal line (a vinculum) or dots above it, e.g. $0.2\ov57=0.257575757 ...$

Every repeating or terminating decimal is a rational number since it can be converted to a fraction.

To convert repeating decimal to fraction follow these steps
**Step 1:**

Set the repeating decimal equal to fraction x:

**Step 2:**

Move the repeating digit(s)/repetend to the left of the decimal point by multiplying the decimal by 10, 100, 1000 etc.

**Step 3:**

Subtract the number from both sides of the equation. This will help you to get rid off the decimal part:

**Step 4:**

Solve the equation for x: