Decimals, Fractions, and Percentages

Standard Form/Scientific Notation

If you had a number like this:

54300000.0

Then you would have to make the number so it is under 10:

5.4300000

But you moved the decimal place 7 places to the left, so the standard form is:

5.43 x 10⁷

HINT

Recurring decimals are written with a little dot or a line above a number to show that it goes on forever.

HINT

Terminating decimals are decimals that eventually stop and are not recurring.

Rounding

When rounding, you round to the nearest number with the amount of decimal places provided. For example:

59.54

The critical digit (last number) determines what the number will be. In this example, the critical digit is 4. 4 or less, let it rest. 5 or more, raise the score. So because the critical digit is 4, you would round the number to 59.5.

8 8                  - 4 SPOTS AFTER THE DECIMAL PLACES

x    2 . 3 4

   1 3 . 7 5 9 2            - Answer

Dividing Decimals

- PUT THE DECIMAL PLACE WHERE IT WOULD GO (LINE IT UP)

HINT

Powers of 10 are 10, 100, 1000, 10000, etc.;

BODMAS

This is BODMAS. When solving an equation, solve in this order:

• Brackets
• Indices
• Division
• Multiplication
• Addition
• Subtraction

Converting Decimals to Fractions

• 0.8 - 8/10            - Simplify if possible
• 0.56 - 56/100        - Simplify if possible
• 0.024 - 24/1000    - Simplify if possible

Converting Fractions to Decimals

• 247/1000 - Put as a decimal (0.247)
• 7/25 - Make 25 a power of 10, you multiply 25 by 4 to make it 100, and 7 because if you multiply the bottom, you have to do the same to the top.
• 5/8 - Because 8 can't be a power of 10, you do 5 ÷ 8 = 0.625 - 0.625 would be the decimal.

Converting Percentages to Decimals

e.g. 35% = 0.35

To convert to a decimal, you have to divide the percentage by 100, meaning you can just move the decimal place 2 spots to the left.

Converting Decimals to Percentages

e.g. 0.78 = 78%

Converting to a percentage is the opposite of converting to a decimal. You have to multiply by 100 by moving the decimal point 2 places to the right.