Digits, columns, rounding and ×/÷ by 10, 100, 1000.
CoreIn almost every paper that tests this subjectAbout 60 seconds a question in the test
The big idea
Every digit’s value depends on its column: ones, tens, hundreds, thousands, ten-thousands and so on. In decimals the columns continue to the right: tenths, hundredths, thousandths.
To round, find the column you are rounding to and look at the digit immediately to its right. 5 or more rounds up; 4 or less rounds down.
Tips that save marks
Underline the rounding column and circle the next digit before deciding.
Multiplying by 10 moves digits one place left. The decimal point never moves.
Watch out for rounding that carries over, e.g. 19,960 to the nearest 100 is 20,000.
A worked example
Round 348,562 to the nearest 1,000.
The thousands digit is 8.
The next digit (hundreds) is 5 → round up.
Answer: 349,000.
Now try five
Try each one before you look at the answer: answering from memory is what makes it stick. Tap an option to check it. Most children get three or four right at first; five out of five means move on to the next topic.
Question 1Aim for about 60 seconds
Layla's old printer prints 0.91 pages a minute on average. A new printer is 1,000 times faster. How many pages a minute does the new printer print?
Show the worked answer
Answer: C, 910
How to work it out
Multiplying by 1,000 moves every digit 3 places to the left: 0.91 × 1,000 = 910.
Why the other options are wrong
A (9,100): The digits moved one place too many.
B (1000.91): This adds 1,000 instead of multiplying.
D (91): The digits moved one place too few.
E (0.00091): This divides by 1,000; faster means more pages, so multiply.
Question 2Aim for about 60 seconds
In 8,662,918, what is the value of the digit in position 4 from the left?
The digit is 2.
Show the worked answer
Answer: A, 2000
How to work it out
Count the columns from the right: the 2 sits in the 1,000s column, so it is worth 2,000.
Question 3Aim for about 60 seconds
In 6,588,422, what is the value of the digit in position 4 from the left?
The digit is 8.
Show the worked answer
Answer: B, 8000
How to work it out
Count the columns from the right: the 8 sits in the 1,000s column, so it is worth 8,000.
Question 4Aim for about 60 seconds
Round 43,906 to the nearest 1,000.
Show the worked answer
Answer: C, 44000
How to work it out
Look at the digit to the right of the 1,000s column.
5 or more rounds up, less rounds down.
43,906 rounds to 44,000.
Question 5Aim for about 60 seconds
The temperature at midnight was −11°C. By noon it had risen by 17 degrees. What was the temperature at noon?
Show the worked answer
Answer: B, 6°C
How to work it out
Start at −11 and count up 17: 11 degrees takes you to 0°C, and 6 more takes you to 6°C.
Why the other options are wrong
A (28°C): This adds 11 to 17 instead of starting at −11.
C (−6°C): The sign is the wrong way round.
D (17°C): This is only the rise; it has to start from −11°C.
E (−28°C): This goes down instead of up. A rise means count up.
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