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When we divide a whole number by a power of 10, theĪnswer will have as many decimal digits are there are 0's.Īgain, as in Lesson 2, consider this array:Īs we move up the list - as we push the digits one place right - the number has been divided by 10 because each place to the right is worth 10 times less. Starting from the right of 265, separate one decimal digit. Starting from the right of the whole number, separate as How do we divide a whole number by a power of There are no 0's to chop off We will see that we must place a decimal point to Now in Lesson 2 we saw that when a whole number ends in 0's, weīut when a whole number does not end in 0's - as 265 - then
#POWER OF TEN RULE HOW TO#
These example illustrate that, whenever we multiply or divideīy a power of 10, the digits do not change We simply move the decimal pointįinally, we must see how to divide a whole number by a
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Move the decimal point left as many places as How do we divide a decimal by a power of 10? Since money has two decimal digits, we added on a 0. Since 50 pounds are ten times 5 pounds, they will cost ten Pounds of sugar cost $2.79, how much will 50 pounds cost?Īnswer. The answer is a whole number, 732, which we write without a decimal However, since all the digits fall to the left of the decimal point, Move the decimal point right as many placesĪs there are 0's in the power. Then the power on 10 has to be 11: eleven, because thats how many places the decimal point needs to be moved, and negative, because Im dealing with a. How do we multiply a decimal by a power of 10? The student should let go of that written method immediately. Multiply the following and leave the answers in powers of ten. To multiply powers of ten, add the exponents. But it is not skillful, and it does not take advantage of positional numeration. Since our number system is based on powers of ten, you should understand the notation and how to work with these powers, as follows: 10 0 1. Traditional multiplication would eventually give the right answer (we hope). How do we multiply a whole number by a power of 10?Īdd on as many 0's as appear in the power.ĭoing that is an example of skill in arithmetic, which is to be able to do a problem as quickly and as easily as possible.
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Then you divide the powers of ten by subtracting the exponents. You begin by dividing the numbers that aren’t powers of 10 (the a in a x 10 n). In order to divide numbers in scientific notation, you once again apply the properties of numbers and the rules of exponents. Multiply using the Product Rule and add the exponents.
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Group the powers of 10 using the associative property of multiplication. Multiply the powers of 10, using the Product Rule-add the exponents.Ĭonvert 23.37 into scientific notation by moving the decimal point one place to the left and multiplying by 10 1. Regroup, using the commutative and associative properties. You may notice that the decimal point was moved five places to the right until you got the number 4, which is between 1 and 10. To write a small number (between 0 and 1) in scientific notation, you move the decimal to the right and the exponent will have to be negative. You moved the decimal point 6 spots to the left, creating the decimal 0.00000100357. Remember that the zeroes in between 1 and 3 must also be included in the final number. You moved the decimal point the correct number of spaces, but the number you created is different than the number you started with: 1.00357 x 10 -6 ≠ 0.000001357. You moved the decimal point in the correct direction, but you did not move it enough places. You added six 0s to the end of the decimal.