Video: Comparing Expressions by Multipliying Decimals and Dividing Integers by Powers of 10

Which of the following is equal to 0.04347 × 100? [A] 434700 ÷ 10 [B] 434700 ÷ 100000 [C] 43470 ÷ 1000 [D] 4347000 ÷ 10

05:30

Video Transcript

Which of the following is equal to 0.04347 multiplied by 100? We have four possible answers, 434700 divided by 10, 434700 divided by 100000, 43470 divided by 1000, or 4347000 divided by 10.

Before we think about what each of these calculations is worth, there’s something interesting about all of them. Whether it’s the multiplication in the question or the four divisions in the answers, each of the calculations involves multiplying or dividing by powers of 10.

By a power of 10, we mean 10, 100, 1000, and so on. So, when we multiply or divide by these numbers, if we remember the digits in the number we’re multiplying by 10 or 100 or 1000, the digits shift. We can show how the digit shift by using a place value table. So, let’s do that as we work out what the value of the multiplication in the question is.

When we multiply a number by 10, 100, or 1000, the digits shift to the left and the number gets larger. We don’t need to worry about the zero oneths, or the zero tenths. So, let’s start with our first significant digit which is four, four hundredths. If we multiply the value four hundredths by 100, the digit four has a value 100 times greater. And so, it will shift from the hundredths column past the tenths column to the ones column.

A good way to remember how many times to shift the digits is to look at the number we’re multiplying by. 100 has two zeros and this gives us a clue that we need to shift the digits two places. Let’s shift the rest of the digits two places.

Three thousandths shifts two places to the tenths column. Four ten-thousandths shifts two places to the hundredths column. And seven hundred-thousandths shifts two places to the thousandths column. And so, really what our question is asking is which of the following is equal to 4.347. Let’s look at our four calculations to find out which one is correct.

Before working any of the answers out we can see that two of the calculations are not going to give us an answer that is the same as 4.347. The first and the last calculations on our list are both dividing by 10. 10 has one zero. So, as we shift the digits of these numbers, they’re only going to move one place. And we can see that if you move these digits one place, we’re not going to get a number that is the same as 4.437. So, we don’t actually need to work out the answers to these two.

The digits move more than once in our other two calculations. So, let’s see which of these two is the correct answer. In our first calculation, we need to work out 434700 divided by 100000. The number 100000 has five zeros. So, this gives us a clue that we need to shift the digits five places. Because we’re dividing, we shift the digits to the right. So, the number becomes smaller.

As we shift all the digits five places to the right, the two zeros will be part of a decimal number on the end. And they won’t have any value. So, we don’t need to think about those. Let’s just shift these four digits five places to the right, one, two, three, four, and five, 4.347 which is the number we’re looking.

Let’s just quickly check that we’ve got the correct answer by calculating the final division. 43470 divided by 1000. 1000 has three zeros in. So, we know that we have to shift the digits three places. And we’re going to shift them to the right again, so that the number becomes smaller because we’re dividing. And if we shift the digits three places to the right, we get an answer a 43.47, which is not the same as the number we’re looking for. And so, which of the following is equal to 0.04347 multiplied by 100? It’s the calculation 434700 divided by 100000.

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