# Decimal numbers

This page will be about Decimal numbers. We will talk about tenths, hundredths, and thousandths.

1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

Billions | Hundred millions | Ten millions | Millions | Hundred Thousands | Thousands | Hundreds | Tens | Ones | And | Tenths | Hundredths | Thousandths | Ten Thousandths | Hundred Thousandths | Millionths | Ten Millionths |

The Above Chart specifies the places of the decimal number system from the billions place to the ten millionths place. There is a period where the and is in the table. The number represented in the table is 100,000,000,000,000.000 - one hundred billion. Given an arbitrary number say 3.36, the first three is in the ones place, the next three in the tenths place, and the six in the hundredths place, the number is read three point three six and means three and three over thirty-six hundred.

Rules:

- Read the whole part
- Say and for the decimal point
- Read the decimal part
- Say the place value of the last digit

# Comparing decimals

If you need to tell what decimal digit is larger you make them all have the same number of digits by adding a zero to smaller one for example:

- If you compare .266 to.25, add a zero to .25 making it .250. Now you can see that .250 is smaller than .266
- If you compare .4 to .466, add two zeros to point four making it .400 and you can see .400 is smaller than .400

# Rounding decimals

You round a decimal by seeing if the next place in the decimal is .5 or greater, if it is .5 or greater then you round to the next number. If it is smaller than .5 then you drop the remaining digits. Example:

- 2.25 rounded becomes 2.3
- 2.24 rounded becomes 2.2
- 10.567 rounded becomes 10.57
- 10.564 rounded becomes 10.56

# Scientific notation

The number system is based on multiples of ten. Scientific notation uses this idea of based ten numbers to give a shorter way to write very big numbers and very small numbers. 100,000 can be written ten to the fifth. (10^{5}) The number .00098 can be expressed in scientific notation as 9.8 x 10 ^{-4}. The rules for this are as follows:

- Take the number and express it in single digit
- Put a decimal point
- Write the next number
- Put times ten to the appropriate number

# Adding and subtracting decimals

- Line up the decimal points
- Be sure the whole numbers are to the decimal point
- Add or subtract the numbers
- Bring the decimal point straight down in the answer

Examples: