what does round to 3 decimal places mean
Lesson 12 Department 2
HOW TO Round OFF A DECIMAL
HOW TO Express THE QUOTIENT
AS A DECIMAL
Department 1 of this Lesson.
Calculator problems
| 4. | How practise we round off, or approximate, a decimal to a required number of decimal digits? |
$6.73 8  $6.vii4 | |
| Await at the digit to the right of the required number. If information technology is a five or greater, add i to previous digit. If it is less than 5, leave the previous digit unchanged. In either case, drib all the remaining digits. | |
Case 1. Round off this decimal vii.253896 to three decimal digits.
Answer. 7.253 896
7.25four
(The wavy equal sign 
means "is approximately equal to.")
To round off to three decimal digits, nosotros must look at the digit in the 4th place. The digit in the quaternary place is 8 (greater than v). Therefore, we add together 1 to the previous digit 3.
Example 2. Round off 7.253896 to two decimal digits.
Respond. 7.2five 38967.25
The digit in the third decimal place is three (less than 5). Therefore, we leave the digit in the second identify (5) unchanged.
Instance 3. Round off 7.253896 to the nearest tenth.
Answer. 7. 2 538967. three
To round off to the nearest tenth, ways to go along one decimal digit. (To round off to the nearest hundredth would mean to go along two digits; to the nearest thousandth, three; and so on. Lesson 3, Question 5.)
At present, the digit in the 2nd decimal place is 5. Therefore add i to the previous digit two.
Instance 4. Round off $6.497014
Reply. This is coin. Therefore we must round off to two decimal digits:
$6. 49 7014$half dozen. 50
The digit in the tertiary decimal identify is 7 (greater than 5). Therefore, when nosotros add together 1 to 9 of 6. 49, we get 6. 50
To round off whole numbers, encounter Lesson two.
| 5. | How practise we express the quotient every bit a decimal? | ||
 | |||
| When in that location are no more digits in the dividend: | |||
| 1) | Identify a decimal point and bring it up to the caliber. | ||
| 2) | Add a 0 onto the residual, and continue dividing. | ||
| 3) | Add together a 0 onto each remainder until the division is verbal. If the division volition never be exact, round off the quotient to the required number of decimal digits. | ||
Begin,
"4 goes into 32 8 (8) times.
"4 goes into seven one (i) time with 3 left over.
There are no more digits in the dividend. Therefore, according to the rule: Place a decimal point, bring it upward to the quotient, and add together a 0 onto the remainder3:
Keep dividing. Identify a 0 later on each remainder:
The caliber of 327 ÷ 4, and so, may exist expressed in three different ways:
Example 6. Compare the following:
| a) | If information technology takes 4 yards of material to cover a sofa, how many sofas could y'all cover with 25 yards? |
| b) | If 4 people go to luncheon and the bill is $25, how much does each 1 pay? |
Solution.
a) We must divide by 4:
"4 goes into 25 six (half dozen) times with i left over."
This means that you could comprehend half-dozen sofas, and 1 thou of material volition remain.
| b) | Again, we must split up by 4, merely here we must express the quotient as a decimal -- as money -- and 6 R 1 makes no sense. |
Each person volition pay $6.25.
Solution. "half dozen goes into 12 2 (two) times. 6 goes into 7 one (i) time with i left over." Place a decimal signal, and add a 0 onto the remainder ane:
Now the same balance 4 will be repeated. Therefore this partition will never be verbal. To round off to three decimal digits, and then, nosotros must know the digit in the fourth place -- 6. Therefore, nosotros add 1 to the previous digit; we become 21.167
To circular off, we must know one more decimal digit
than is required.
| 6. | How do nosotros proceed when the divdend is less than the divisor? |
| 5 ÷ viii | |
| Proceed as in the previous instance. | |
Case 8. 5 ÷ eight
The dividend 5 is less than the divisor viii. Since 8 is the divisor, write it outside the division box:
"8 goes into 5 nothing (0)." Identify the decimal signal, and add on a 0.
Adjacent, "viii goes into 50 vi (6) times (48) with 2 left over."
"8 goes into 20 two (2) times (xvi) with 4 left over."
"8 goes into xl 5 (five) times exactly."
Nosotros will come across an awarding of the dividend less than the divisor when we come to changing a fraction to a decimal (Lesson 24). For,
The horizontal line separating five and 8 is the partition bar.
Instance 9. The post-obit division will not exist verbal. Round it off to three decimal digits:
1 ÷ xi
Solution. Identify 11 outside the box and begin:
"xi goes into 1 cypher (0)." Identify the decimal betoken, and add together on a 0.
Now 11 does not become into ten. Write 0 in the caliber --
-- and add another 0 onto the dividend.
"eleven goes into 100 nine (9) times, with 1 left over."
Write 9 in the caliber, and add together a 0 onto the remainder 1.
Write 0 in the quotient, and add another 0 to the dividend. Once again,
This partitioning will never be exact. We will go along getting 090909. To round it off to three digits, we accept calculated the digit in the fourth place. It's nine. Therefore, we will add 1 to the previous digit:
0.0909 0.091
Yous sometime see: 1 ÷ 11 = 0.090909... The iii dots, called ellipsis, hateful: "The decimal for 1 ÷ 11 will never be exact. However, we tin gauge it to as many decimal digits as we please past post-obit the pattern 090909."
Estimator issues
Example 10. Patricia pays $66 each year for mag subscriptions. How much does that toll her each week?
Solution. Nosotros must carve up $66 by the number of weeks in a year, 52. Press
Run into
Since this is money, we must circular it off to the nearest cent.
1.two6 92307$one.2seven
It costs Patricia approximately $1.27 each calendar week.
Example 11. A plane flew between New York and Los Angeles, a distance of 2,477 miles, in 4.25 hours. What was its speed in miles per 60 minutes?
Solution. Miles "per" hour indicates Miles ÷ hours (Lesson 11). Press
| two | 4 | seven | 7 | ÷ | 4 | . | 2 | 5 | = |
See
This is approximately 582.eight miles per hour.
Example 12. With a figurer, Janet found that 978 ÷ five = 195.6.
What actually is the residuum upon dividing 978 by 5?
Reply. three.
The quotient, 195.6, is what number times five will equal 978. (Lesson 11).
| 195.six × 5 | = | 195 × 5 +.6 × 5 | (Lesson 9) |
| = | 975 + three. | (Lesson 10) | |
3 is the residuum.
This example illustrates the pregnant of a decimal quotient.
It consists of a whole number, 195, plus a decimal fraction, .six. (Lesson 3.)
The digit to the correct of the decimal point is not the residue..6 is that decimal fraction of the divisor. (Lesson 27.)
Please "plough" the page and do some Problems.
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