Place value, ordering and rounding
Multiplying and dividing decimals mentally
Multiply decimals can be tricky yet it can be as simple as multiplying whole numbers. My steps on multiplying decimals:
count how many digits available after the decimal point from numbers you want to multiply. Store that info.
ignore the decimal point (the decimal numbers become whole numbers). Do the multiplication between numbers.
return the decimal point based on the info from step 1
For example: 0.3 x 5. (1) In total from these two numbers, we have 1 digit behind the decimal point. It means the result will have 1 digit behind the decimal point. (2) ignore the decimal point of these 2 numbers. 3 X 5 = 15. (3) return the decimal point. How many digit behind the decimal point is for the result? 1. So the answer is 1.5.
Another example : 0.04 x 1.2. (1)In total, we have 3 digits behind the decimal point. It means the result of this calculation will have 3 digits behind the decimal point. (2) ignore the decimal point. 4 x 12 = 48. (3) Based on step 1, the result will have 3 digits behind the decimal point. Hm, the result only has 2 digits! No worries, just add 0 . The result is 0.048.
For dividing decimal, I will use my knowledge on fraction and equivalent fraction . My steps on dividing decimals:
write them as a fraction
find the equivalent fraction with the goal of eliminating decimal point
do the division
Exercise time ! Work these out mentally. The answer will be available at the end of the post.
1.3 x 0.02
24 : 0.04
(12 x 0.2) : (0.3 x 0.2)
Multiplying and dividing by powers of 10
Things you need to remember about powers of 10
Multiply a number by the power of 10 with the negative index is the same as divide the number by the power of 10.
Divide a number by the power of 10 with the negative index is the same as multiply the number by the power of 10.
Exercise :
Rounding
For this topic, you need to understand about the place value, significant figure and decimal place. We jump directly to the example.
If, I want to round 3 451.67 to the nearest whole number, it means I will keep the number until 3 451. Yet, there is a possibility that the last digit 1 changes. Depending on the digit after 1. If the digit after 1 is 5 or more, the last digit of the number will be increased by 1. If not, stay the same. Look on the number, after 1 we have 6. It is more than 5. So the last digit is increased by 1. The result is 3 452. The result will be until the digit that takes the position of the nearest whole number.
Another example using the same number. I will round the number to 3 significant figures (3 S.F.). I will keep the number until 3 45. Now, check the digit after 5. 1 is less than 5, stay the same. After that, check the original value position of 5. It is ten. On the result, 3 45, the 5 takes the position of one. Hm, we need to add something so the 5 takes the position of 10. Yeah, we need to add a 0 after 5. The result is 3 450.
Order of operations.
BEDMAS : Bracket, Exponention (power), Division Multiplication and Addition Subtraction.
Note: if you have division and multiplication or addition and subtraction on the same problem, you need to do it from left to right.
I will give you a problem : work out the value of this expression when x = 2 and y = -3 for 4x^2 - y
The answer is 0.026 ; 600 ; 40 ; 15 000 ; 0.012 ; 342 000 ; 19
See you !