We already know how to find We join together and :
To see why this works, we can use a place value chart.
Step 1: First, we write down the place value chart for :
| ten thousands | thousands | hundreds | tens | ones |
Step 2. Since we're multiplying by we move all digits to the left by place and place a zero in the empty cell on the right.
| ten thousands | thousands | hundreds | tens | ones |
We conclude that
This process works because a digit in a given place value is times smaller than the same digit one place value to the left. Therefore, to multiply a number by we move all of the digits by one place to the left.
Use a place value chart to calculate the value of
Step 1. We write down the place value chart for :
| ten thousands | thousands | hundreds | tens | ones |
Step 2. Since we're multiplying by we move all digits to the left by place and place a zero in the empty cell on the right.
| ten thousands | thousands | hundreds | tens | ones |
Therefore,
From left to right, what are the missing digits in the place value chart below for the value of $325 \times 10?$
| ten thousands | thousands | hundreds | tens | ones |
| $0$ | $3$ | $2$ | $\fbox{$\phantom{0}$}$ | $\fbox{$\phantom{0}$}$ |
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a
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$5$ and $0$ |
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b
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$2$ and $0$ |
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c
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$0$ and $0$ |
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d
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$3$ and $0$ |
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e
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$1$ and $0$ |
Complete the place value chart below for the value of $237 \times 10.$
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b
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c
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Suppose that we want to find using a place value chart. We proceed as follows:
Step 1. We write down the place value chart for :
| ten thousands | thousands | hundreds | tens | ones |
Step 2. Since contains a block of zeros, we move all of the digits to the left by spaces and place zeros in the empty cells on the right.
| ten thousands | thousands | hundreds | tens | ones |
We conclude that
This works because multiplying a number by is the same as multiplying by twice, which means that we move to the left by two places.
From left to right, what are the missing digits in the place value chart below for the value of
| ten thousands | thousands | hundreds | tens | ones |
Step 1: We write down the place value chart for :
| ten thousands | thousands | hundreds | tens | ones |
Step 2: Since contains a block of zeros, we move all values to the left by places and place zeros in the empty cells on the right.
| ten thousands | thousands | hundreds | tens | ones |
Therefore, the missing digits are and
From left to right, what are the missing digits in the place value chart below for the value of $516 \times 100?$
| ten thousands | thousands | hundreds | tens | ones |
| $5$ | $\fbox{$\phantom{1}$}$ | $6$ | $0$ | $\fbox{$\phantom{0}$}$ |
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a
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$1$ and $0$ |
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b
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$1$ and $6$ |
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c
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$5$ and $1$ |
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d
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$6$ and $0$ |
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e
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$5$ and $0$ |
Complete the place value chart below for the value of $287 \times 100.$
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a
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b
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c
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A power of is a whole number where the leading digit is one, and the remaining digits are all zero.
For example, the following numbers are all powers of
Using a place value chart, we can multiply a number by any power of ten.
For example, suppose that we want to compute We proceed as follows:
Step 1. We write down the place value chart for :
| ten thousands | thousands | hundreds | tens | ones |
Step 2. We count the zeros in the power of Our power of ten is which contains a block of zeros. Therefore, we move all digits by places to the left and place zeros in the empty cells on the right.
| ten thousands | thousands | hundreds | tens | ones |
Therefore,
From left to right, what are the missing digits in the place value chart below for the value of
| ten thousands | thousands | hundreds | tens | ones |
We proceed as follows:
Step 1. We write down the place value chart for :
| ten thousands | thousands | hundreds | tens | ones |
Step 2. Notice that contains a block of zeros. So, we move all digits to the left by places and place zeros in the empty cells on the right.
| ten thousands | thousands | hundreds | tens | ones |
Therefore, the missing digits are and
Complete the place value chart below for the value of $3 \times 1,000.$
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b
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c
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Complete the place value chart below for the value of $64 \times 1,000.$
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