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Rounding numbers is a useful math skill that simplifies numbers to make calculations easier. When rounding, you adjust a number to the nearest ten, hundred, or another place value. This is helpful for quick estimates. To round a number, first determine which place value you're rounding to. Look at the digit immediately to the right of your target.
If this digit is 5 or greater, round up by adding 1 to the target place. If it's less than 5, round down. For example, in rounding 68 to the nearest ten, observe that the last digit is 8. Since 8 is greater than 5, you round up to make 68 into 70. Similarly, with 826 rounded to the nearest hundred, focus on the last two digits, 26. Because 26 is less than 50, round down for a result of 800.
This adjustment simplifies numbers while maintaining reasonable accuracy for estimation purposes.

Multiplication is one of the basic operations in math, representing repeated addition. It involves two numbers: a multiplier and a multiplicand. The product is the result you get after multiplying these numbers together. When estimating products, rounding makes multiplication easier by handling simpler numbers. Take the rounded numbers from our previous section: 70 and 800. These rounded figures are easier to work with. Multiply them as you would smaller numbers, aligning their positions:

• Multiply 70 by 8 first gives 560 (since 70 * 8 = 560).
• Add the two zeros from the factor 800 (800 = 8 * 100), resulting in 56,000.

This way, you perform multiplication in manageable steps, providing an estimated product of 56,000.

Calculating the actual product involves multiplying the original numbers without rounding them. This step confirms your estimations by showing the true value of the multiplication. It requires careful multiplication, especially when dealing with larger numbers like 68 and 826. First, multiply the numbers as they are:

• Begin with units: 68 multiplied by 6 (from 826), add 68 multiplied by 20 (for the tens), and finally by 800 (for the hundreds).
• This may involve breaking it down into smaller, more manageable calculations.

After performing these operations, the actual product of 68 * 826 is found to be 56,168.
The exercise highlights that while estimates through rounding are useful, calculating the actual product ensures precision and leads to a deeper understanding of the magnitude of numbers involved in the calculation.