Multiplying by 10
Multiplying by 10 in Grade 4 math uses a simple shortcut: append a zero to the right end of any whole number to get its product with 10. For example, 45 × 10 = 450. Taught in Chapter 6 of Saxon Math Intermediate 4, this rule works because our base-10 number system shifts every digit one place to the left when multiplied by 10. Mastering this shortcut is essential for mental math and for understanding multiplication by multiples of 10 and 100 in higher grades.
Key Concepts
Property To multiply any whole number by 10, there is a simple and effective shortcut you can use for quick mental math. You just take the original number and place a single zero at the very end of it. This method instantly gives you the correct product without needing to perform the full multiplication process.
Example Example 1: To find out how many people pass through a gate in 10 minutes at a rate of 100 people per minute, you multiply $100 \times 10$. Just add a zero to 100 to get $1000$ people. Example 2: If you have 45 packs of trading cards and each pack has 10 cards, you can find the total by calculating $45 \times 10 = 450$ cards.
Explanation Multiplying by 10 is like a magic trick! You don't need a calculator, just a zero. Take any number, add a zero to its right side, and voilà—you've made it ten times bigger. It is a handy shortcut that makes you look like a math wizard and works every single time for whole numbers.
Common Questions
How do you multiply a whole number by 10?
Add a zero to the right end of the whole number. For example, 63 × 10 = 630 and 100 × 10 = 1,000.
Why does multiplying by 10 add a zero?
Our number system is base 10, so multiplying by 10 shifts every digit one place to the left, leaving the ones place empty—which we write as zero.
Does the multiply-by-10 shortcut work for decimals?
For decimals, multiplying by 10 moves the decimal point one place to the right instead of adding a zero. For example, 3.5 × 10 = 35.
When do Grade 4 students learn multiplying by 10?
Students learn this shortcut in Grade 4, Chapter 6 of Saxon Math Intermediate 4. It builds directly on place value understanding from earlier chapters.
How does multiplying by 10 relate to multiplying by 100 or 1,000?
The same idea extends: multiplying by 100 appends two zeros, and multiplying by 1,000 appends three zeros. The number of zeros added equals the number of zeros in the multiplier.
What is a real-world use of multiplying by 10?
Converting dollars to dimes (1 dollar = 10 dimes), or calculating the cost of 10 identical items are everyday uses of multiplying by 10.