MULTIPLYING & DIVIDING
23.6 multiplied by 100 = ?
= 2 360
Working out:
We are multiplying by 100, which means we move each digit 2 places to the left in the place value columns (because 100 has 2 zeros).
2 (in tens) → now in thousands
3 (in ones) → now in hundreds
6 (in tenths) → now in tens
The digits get 10× bigger for each place moved, so the number becomes 2 360.
53.91 divided by 1 000 = ?
0.05391
Working out:
We are dividing by 1 000, which means we move each digit 3 places to the right in the place value columns (because 1 000 has 3 zeros).
5 (in tens) → now in hundredths
3 (in ones) → now in thousandths
9 (in tenths) → now in ten-thousandths
1 (in hundredths) → now in hundred-thousandths
The digits become 10× smaller each time they move, so the number becomes 0.05391
7.04 multiplied by 1 000 = ?
7 040
Working out:
We are multiplying by 1 000, so we move each digit 3 places to the left in the place value columns.
7 (in ones) → now in thousands
0 (in tenths) → now in hundreds
4 (in hundredths) → now in tens
The digits shift to larger place value columns, making the number 7 040.
4 500 divided by 100 = ?
45
Working out:
We are dividing by 100, so we move each digit 2 places to the right in the place value columns.
4 (in thousands) → now in tens
5 (in hundreds) → now in ones
The zeros shift with the digits but no longer hold value after the decimal
The number becomes 45.
0.006 multiplied by 100 = ?
0.6
Working out:
We are multiplying by 100, which means we move each digit 2 places to the left in the place value columns.
6 (originally in the thousandths) → now in the tenths
The digits shift to bigger place value columns, so 0.006 becomes 0.6
Convert 0.1 into a fraction
0.1 = 1/10
The digit 1 is in the tenths place, which means it's out of 10.
So:
0.1 = 1 ÷ 10 = 1/10
Convert 0.01 into a fraction
0.01 = 1/100
The digit 1 is in the hundredths place, which means it's out of 100.
So:
0.01 = 1 ÷ 100 = 1/100
Convert 10 into a fraction
10 = 10/1
Any whole number can be written as a fraction by putting it over 1.
So:
10 = 10 ÷ 1 = 10/1
Convert 0.001 into a fraction
0.001 = 1/1 000
The digit 1 is in the thousandths place, which means it's out of 1 000.
So:
0.001 = 1 ÷ 1 000 = 1/1 000
Convert 0.0001 into a fraction
0.0001 = 1/10 000
The digit 1 is in the ten-thousandths place, which means it's out of 10 000.
So:
0.0001 = 1 ÷ 10 000 = 1/10 000
If I want to turn 26.7 into an answer that includes 26 thousands, what is the mathematical process I need to use?
Be specific with the type of process used and how much when using that process.
Multiply by 1000 (one thousand). 26 700.
26.7 = 2 in the tens column, 6 in the ones column and 7 in the tenths column.
26.7 x 100 means I shift the numbers 3 places to the left. This will move the numbers in larger place value columns.
So:
·2 (in tens PV column) → now in Ten Thousands PV column
·6 (in ones PV column) → now in Thousands PV column
·7 (in tenths PV column) → now in Hundreds PV column
If I want to turn 3.45 into an answer that includes 345 hundreds, what is the mathematical process I need to use?
Be specific with the type of process used and how much when using that process.
Multiply by 10,000 (ten thousand). 34,500.
3.45 = 3 in the ones column, 4 in the tenths column and 5 in the hundredths column.
3.45 × 10,000 means I shift the numbers 4 places to the left. This will move the digits into larger place value columns.
So:
· 3 (in ones PV column) → now in Ten Thousands PV column
· 4 (in tenths PV column) → now in Thousands PV column
· 5 (in hundredths PV column) → now in Hundreds PV column
Another way to look at it: 345 hundreds means 345 groups of 100, which means 345 times by 100.
If I want to turn 0.382 into an answer that includes 382 tens, what is the mathematical process I need to use?
Be specific with the type of process used and how much when using that process.
Multiply by 1,000 (one thousand). 382.
0.382 = 3 in the tenths column, 8 in the hundredths column and 2 in the thousandths column.
0.382 × 1,000 means I shift the numbers 3 places to the left into larger place value columns.
So:
· 3 (in tenths PV column) → now in Hundreds PV column
· 8 (in hundredths PV column) → now in Tens PV column
· 2 (in thousandths PV column) → now in Ones PV column
Another way to look at it: 382 tens = 382 groups of 10 = 382 x 10, which = 3820. To get from 0.382 to 3820, you need to multiply the number by 1000.
If I want to turn 1.208 into an answer that includes 1,208 ones, what is the mathematical process I need to use?
Be specific with the type of process used and how much when using that process.
Multiply by 1,000 (one thousand). 1,208.
1.208 = 1 in the ones column, 2 in the tenths column, 0 in the hundredths column, and 8 in the thousandths column.
1.208 × 1,000 means I shift the digits 3 places to the left into larger place value columns.
So:
· 1 (in ones PV column) → now in Thousands PV column
· 2 (in tenths PV column) → now in Hundreds PV column
· 0 (in hundredths PV column) → now in Tens PV column
· 8 (in thousandths PV column) → now in Ones PV column
If I want to turn 7.9 into an answer that includes 790 tens, what is the mathematical process I need to use?
Be specific with the type of process used and how much when using that process.
Multiply by 1,000 (one thousand). 1,208.
1.208 = 1 in the ones column, 2 in the tenths column, 0 in the hundredths column, and 8 in the thousandths column.
1.208 × 1,000 means I shift the digits 3 places to the left into larger place value columns.
So:
· 1 (in ones PV column) → now in Thousands PV column
· 2 (in tenths PV column) → now in Hundreds PV column
· 0 (in hundredths PV column) → now in Tens PV column
· 8 (in thousandths PV column) → now in Ones PV column
If I want to turn 47.321 into an answer that has 47 in the thousandths, what is the mathematical process I need to use?
Be specific with the type of process used and how much when using that process.
Divide by 1 000 (one thousand). 0.047321
47.321 = 4 in the tens column, 7 in the ones column, 3 in the tenths column, 2 in the hundredths column, and 1 in the thousandths column.
47.321 ÷ 1 000 means I shift the numbers 3 places to the right. This will move the digits into smaller place value columns.
So:
· 4 (in tens PV column) → now in Hundredths PV column
· 7 (in ones PV column) → now in Thousandths PV column
· 3 (in tenths PV column) → now in Ten-Thousandths PV column
· 2 (in hundredths PV column) → now in Hundred-Thousandths PV column
· 1 (in thousandths PV column) → now in Millionths PV column
If I want to turn 348.2 into an answer that has 3 in the tenths column, what is the mathematical process I need to use?
Be specific with the type of process used and how much when using that process.
Divide by 1 000 (one thousand). 0.3482
348.2 = 3 in the hundreds column, 4 in the tens column, 8 in the ones column, and 2 in the tenths column.
348.2 ÷ 1 000 means I shift the numbers 3 places to the right, into smaller value columns.
So:
· 3 (in hundreds PV column) → now in Tenths PV column
· 4 (in tens PV column) → now in Hundredths PV column
· 8 (in ones PV column) → now in Thousandths PV column
· 2 (in tenths PV column) → now in Ten-Thousandths PV column
If I want to turn 6.2741 into an answer that has 6 in the ten-thousandths, what is the mathematical process I need to use?
Be specific with the type of process used and how much when using that process.
Divide by 10 000 (ten thousand). 0.00062741
6.2741 = 6 in the ones column, 2 in the tenths column, 7 in the hundredths column, 4 in the thousandths column, and 1 in the ten-thousandths column.
6.2741 ÷ 10 000 means I shift the numbers 4 places to the right into smaller place value columns.
So:
· 6 (in ones PV column) → now in Ten-Thousandths PV column
· 2 (in tenths PV column) → now in Hundred-Thousandths PV column
· 7 (in hundredths PV column) → now in Millionths PV column
· 4 (in thousandths PV column) → now in Ten-Millionths PV column
· 1 (in ten-thousandths PV column) → now in Hundred-Millionths PV column
If I want to turn 543 000 into an answer that has 543 in the thousands column, what is the mathematical process I need to use?
Be specific with the type of process used and how much when using that process.
Divide by 100 (one hundred). 5 430
543 000 = 5 in the hundred-thousands column, 4 in the ten-thousands column, and 3 in the thousands column.
543 000 ÷ 100 means I shift the digits 2 places to the right into smaller value columns.
So:
· 5 (in hundred-thousands PV column) → now in Thousands PV column
· 4 (in ten-thousands PV column) → now in Hundreds PV column
· 3 (in thousands PV column) → now in Tens PV column
· Remaining zeros adjust accordingly
If I want to turn 8 000 000 000 into an answer that has 8 in the tenths column, what is the mathematical process I need to use?
Be specific with the type of process used and how much when using that process.
Divide by 10 000 000 000 (ten billion). 0.8
8 000 000 000 = 8 in the billions column.
8 000 000 000 ÷ 10 000 000 000 means I shift the digit 10 places to the right into smaller place value columns.
So:
· 8 (in billions PV column) → now in Tenths PV column
347 multiplied by ten to the power of 2 = ?
34 700
Working out:
Ten to the power of 2 means 10 × 10 = 100.
Multiplying by 100 means we move each digit 2 places to the left in the place value columns.
3 (in hundreds) → now in ten-thousands
4 (in tens) → now in thousands
7 (in ones) → now in hundreds
The digits move into larger place value columns, making the number 100 times bigger.
Final answer: 34 700
129.4 divided by ten to the power of 3 = ?
0.1294
Working out:
Ten to the power of 3 means 10 × 10 × 10 = 1 000.
Dividing by 1 000 means we move each digit 3 places to the right in the place value columns.
1 (in hundreds) → now in tenths
2 (in tens) → now in hundredths
9 (in ones) → now in thousandths
4 (in tenths) → now in ten-thousandths
Digits move to smaller value columns, making the number 1 000 times smaller.
Final answer: 0.1294
502.8 multiplied by ten to the power of 4 = ?
5 028 000
Working out:
Ten to the power of 4 means 10 × 10 × 10 × 10 = 10 000.
Multiplying by 10 000 means we move each digit 4 places to the left in the place value columns.
5 (in hundreds) → now in millions
0 (in tens) → now in hundred-thousands
2 (in ones) → now in ten-thousands
8 (in tenths) → now in thousands
The digits move into much larger place value columns, making the number 10 000 times bigger.
Final answer: 5 028 000
705 divided by ten to the power of 5 = ?
0.00705
Working out:
Ten to the power of 5 means 10 × 10 × 10 × 10 × 10 = 100 000.
Dividing by 100 000 means we move each digit 5 places to the right in the place value columns.
7 (in hundreds) → now in ten-thousandths
0 (in tens) → now in thousandths
5 (in ones) → now in hundred-thousandths
The digits move to much smaller place value columns, shrinking the number.
Final answer: 0.00705
381.2 multiplied by ten to the power of 6 = ?
381 200 000
Working out:
Ten to the power of 6 means 1 000 000 (a million).
Multiplying by 1 000 000 means we move each digit 6 places to the left in the place value columns.
3 (in hundreds) → now in hundred-millions
8 (in tens) → now in ten-millions
1 (in ones) → now in millions
2 (in tenths) → now in hundred-thousands
The digits increase in value as they shift left, making the number 1 000 000 times bigger.
Final answer: 381 200 000