Math (10)

Negative Powers of 10

A negative power means how many times to divide by the number. Example: 5 × 10^ -3 = 5 ÷ 10 ÷ 10 ÷ 10 = 0.005 Trick: negative powers of 10, move the decimal point to the left. Example: 7.1 × 10 ^ -3 = think "move the decimal point 3 places to the left" :7.1 0.71 0.071 0.0071

Powers of 10

It is a very useful way of writing down large or small numbers. Instead of having lots of zeros, you show how many powers of 10 will make that many zeros Example: 5,000 = 5 × 1,000 = 5 × 10^3

Multiply Decimals

Just follow these steps: 1)Multiply normally, ignoring the decimal points. 2)Then put the decimal point in the answer - it will have as many decimal places as the two original numbers combined. In other words, just count up how many numbers are after the decimal point in both numbers you are multiplying, then the answer should have that many numbers after its decimal point.

Add 3.25, 0.075 and 5

Line the decimals up: 3.25 0.075 + 5. "Pad" with zeros: 3.250 0.075 + 5.000 Add: 3.250 0.075 + 5.000 ______ 8.325

Calculate 7.005-0.55

Line the decimals up: 7.005 - 0.55 "Pad" with zeros: 7.005 - 0.550 Subtract: 7.005 - 0.550 ----------- 6.455

The exponent (or index or power)

The exponent (or index or power) of a number says how many times to use the number in a multiplication. Example: 10^3 = 10 × 10 × 10 = 1,000 In words: 10^3 could be called "10 to the third power", "10 to the power 3" or simply "10 cubed"

TheTrick

The index of 10 says how many places to move the decimal point to the right. Example: What is 1.35 × 10^4 = 1.35 x (10 × 10 × 10 × 10) = 1.35 x 10,000 = 13,500 But it is easier to think "move the decimal point 4 places to the right" 1.35 13.5 135. 1350. 13500.

Dividing Decimal by a Decimal Number

The trick is to convert the number you are dividing by to a whole number first, by shifting the decimal point of both numbers to the right: Now you are dividing by a whole number, and can continue as normal. It is safe to do this if you remember to shift the decimal point of both numbers the same number of places. Example: Divide 6.4 by 0.4 You are not dividing by a whole number, so you need to move the decimal point so that you are dividing by a whole number: move 1 6.4 64 0.4 4 move 1 6.4/0.4 is exactly the same as 64/4, as you moved the decimal point of both numbers. And the answer is: 64 / 4 = 16

Adding Decimals

To add decimals, follow these steps: 1)Write down the numbers, one under the other, with the decimal points lined up 2) If you like, Put in zeros so the numbers have the same length 3)Then add normally, remembering to put the decimal point in the answer

Dividing a Decimal Number by a Whole Number

To divide a decimal number by a whole number: 1)Use Division or Long Division (ignoring the decimal point) 2)Then put the decimal point in the same spot as the dividend (the number being divided) Example: Divide 9.1 by 7 Ignore the decimal point and use Long Division: 13 ___ 7 )91 Put the decimal point in the answer directly above the decimal point in the dividend: 1.3 ____ 7 )9.1 The answer is 1.3

Subtracting Decimals

To subtract decimals, follow these steps: 1)Write down the two numbers, one under the other, with the decimal points lined up. 2)Add zeros so the numbers have the same length 3)Then subtract normally, remembering to put the decimal point in the answer

Example: Multiply 0.03 by 1.1

start with: 0.03 × 1.1 multiply without decimal points: 3 × 11 = 33 0.03 has 2 decimal places, and 1.1 has 1 decimal place, so the answer has 3 decimal places: 0.033