Have you ever paid attention to the headlines on news channels? Let’s have a look at a few examples:
- In a football match that drew 51,000 people to the stadium and 40 million TV viewers globally, the United States drew with Canada.
- During the last climate protest, 500,000 people took the streets to let the government know they are discontent.
Can we confidently assert that the figures reported in the news accurately reflect the number of people involved in these scenarios? No! We are aware that these are not exact figures. The word approximately means that the number was similar to the numbers reported.
Obviously, 51,000 may mean 50,800 or 51,300, but not 70,000. Similarly, 13 million passengers could represent a population of more than 12 million but less than 14 million, but not more than 20 million. The amounts in the examples above are not exact counts, they are estimates. We round numbers to make them easier to work with or to express a number with a reasonable level of precision.
How to round numbers
How to round numbers will depend on the method and situation that calls for an approximate number. These are the most conventional ways of rounding numbers:
- Number to the nearest tens
- Number to the nearest thousand
- Rounding up and down
Numbers to the nearest tens
When rounding numbers to the nearest tens, the digit to the right of the tens place, the unit place, must be evaluated. The number 7486, for example, becomes 7490 when rounded to the nearest tens.
Rounding numbers to the nearest thousand
When rounding integers to the nearest thousand, the digit to the right of the thousand place will determine whether we round up or down. For example, when 15,780 is rounded to the nearest thousand, the result is 16,000.
Rounding up and down
While the term “rounding” is generic, we typically use the terms “round up” or “round down” to indicate whether the number has increased or reduced following rounding. The supplied number is said to be rounded up when the rounded number is increased, and it is said to be rounded down when the rounded number is dropped. If the value of the unit is greater or equal to 5 (𝒳 ≥ 5) then you should round up. If the inverse is true, you should round down.
How do you find the sum difference, product or quotient?
Sum
By rounding off numbers, we can estimate the sum of two or more values. Consider the following example. Let’s round the sum of 87 and 2125 to the nearest tenths and compare it to the real number.
- Solution: The digit at the unit position in the number 87 is 7, and as 7 > 5, the estimated number is 90. The digit at one position in number 2125 is 5, and 5 = 5, hence the estimated number is 2130.
90 + 2130 is the estimated equation and 2220 is, therefore, the estimated sum.
87 + 2125 = 2212 is the actual total. When we compare the two amounts, we discover that 2220 > 2212, indicating that the estimated sum is greater than the actual sum.
As a result, the approximate answer is 2220.
Difference
By rounding off numbers to the greatest place, we can approximate the difference. Let’s round the difference between 54,862 and 55,610 to the nearest thousands and compare it to the real difference.
- Solution: The digit at the hundreds position in the number 54,862 is 8, and 8 > 5, hence the estimated number is increased to 55,000.
The digit at the hundreds position in number 55,610 is 6, and 6 > 5, hence the estimated number is increased to 56,000.
56,000 – 55,000 = 1,000
The actual difference is 748 (55,610 – 54,862). Yet, when we compare the two differences, we can see that 1000 > 748. The estimated difference is more than the actual difference. As a result, the approximate answer is 1000.
Product
By rounding off numbers to the greatest place, we can approximate the product of numbers.
Let’s round up to the nearest hundred 97 x 472.
- Solution: 97 can be rounded to 100, and 472 can be rounded to 500. Therefore, the product estimate is 100 x 500 which equals 50,000. The actual answer is 45,784.
Quotient
By rounding off numbers to the greatest place, we can approximate the quotient of numbers and make mental division easier!
Let’s round up to the nearest hundred the quotient of 4428 ÷ 359.
The number 4428 is rounded to 4400, while the number 359 is rounded to 400.
The quotient estimate is 4400 ÷ 400 which is equal to 11. The real answer is 12.3
What to do if your child doesn’t like school?
Estimation by rounding off the numbers
Following the same guidelines as before, whole numbers are rounded off. Let’s put the rules into practice with the help of an example.
Round 7234 to the closest hundred:
- Step 1: Write down the place value to which the number must be rounded. 7234 must be rounded to the next hundred in this case. As a result, we mark 2 in the location of the hundreds.
- Step 2: Look at the digit to the right of 2, which is the tens position, and underline it. In this example, this number is 3.
- Step 3: Match the underlined digit to the number 5.
- Step 4: If it’s less than 5, all the digits to its right, including it, will be replaced by 0, while the digit in the hundreds position (2) will be left alone. As a result, the number 7234 will be rounded to 7200.
If the number to the right of 2 was 5 or greater, then all the digits to the right of 2 would become 0, and 2 would be increased by 1 to become 3. If the given number was 7268, for example, it would be rounded up to 7300 (to the nearest hundred).
Fractions table for halves, quarters, and eighths with decimal equivalents
Fraction Equivalent Fraction Decimal
1/2 2/4 3/6 4/8 5/10 .5
1/3 2/6 3/9 4/12 5/15 .333
2/3 4/6 6/9 8/12 10/15 .666
1/4 2/8 3/12 4/16 5/20 .25
3/4 6/8 9/12 12/16 15/20 .75
1/5 2/10 3/15 4/20 5/25 .2
1/8 2/16 3/24 4/32 5/40 .125
What is the difference between proper and improper fractions?
Value of estimating fractions
When it comes to proper fractions, estimating (or making an educated guess) can be quite useful. Making a proper estimate will get you on the right track if you’re attempting to communicate an amount. There is, however, a delicate line between making educated guesses and guessing out of thin air. While accuracy is good, you should always attempt to get the precise result of a mathematical operation!
Math tutoring services
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