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Solving SBT Lesson 3: Rounding numbers and estimating the results (C2 Math 7 Horizons)
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Solution 1 page 44 SBT Math 7 Creative horizon episode 1
Round numbers to tens: \(-100\sqrt 3 \);\(50 \pi\)
Solution method
Calculate the numbers and then round.
Detailed explanation
We have: −100\(\sqrt 3 \)=(−100) . 1.732050808…=−173.2050808….
The rounded row digit is 7, the digit immediately after the rounded row is 3 < 5, so we keep the rounded row digit, the unit digit is replaced with zero, the rest of the decimal places are left out. we get:
−100\(\sqrt 3 \)=−100.1,732050808…=−173,2050808…≈−170
We have: 50π=50.3.141592654…=157.0796327…
The rounded row digit is 5, the digit after the rounded row is 7 > 5, so we add 1 unit to the rounded row digit, the unit digit is replaced with zero, the rest of the decimal places are discarded. go, we get:
\(50 \pi\)=50.3.141592654…=157.0796327…≈160
Solve problem 2 page 44 SBT Math 7 Creative horizon episode 1
Round the following numbers to 34th,(59);\(\sqrt 5 \)
Solution method
– For rounded row digits:
- Holds the same if the digit immediately to the right is less than 5;
- Increase by 1 if the digit to the right is greater than or equal to 5.
– For digits after the rounding row:
- Discard if in decimal;
- Replaced by digits 0 if in integer part.
Detailed explanation
We have: 34,(59) = 34,595959…
Rounded row digit is 9, the digit after the rounding row is 5 = 5, so we add 1 unit to the rounded row digit, the decimal places after the rounding row are removed, we get: 34,( 59) = 34.595959… ≈ 34.60.
We have: \(\sqrt 5 \)=2,2360679…
The rounded row digit is 3, the number after the rounded row is 6 > 5, so we add 1 unit to the rounded row digit, the decimal places after the rounding row are removed, we get: \(\ sqrt 5 \)= 2.2360679…≈ 2.24
Solve problem 3 page 44 SBT Math 7 Creative horizon episode 1
a) Let’s say x =\(\sqrt {11} \)= 3.166247… Round x to the thousandths.
b) Round y = 1 435 642.9 to the tens place.
Solution method
a) We round to the 3rd (thousandths) of the decimal.
b) Use the formula to round to the tens of decimal places.
Detailed explanation
a) The digit of the rounded row is 6, the digit after the rounded row is 2 < 5, so we keep the number of the rounded row, the decimal places after the rounded row are removed, we get:
x = \(\sqrt {11} \) = 3.166247… ≈ 3.166.
b) The digit of the rounded row is 4, the digit after the rounded row is 2 < 5, so we keep the rounded row digit, the unit digit is replaced with zero, the decimal places are omitted, we Okay:
y = 1435642.9 ≈ 1435640.
Solution 4 page 44 SBT Math 7 Creative horizon episode 1
a) Round a = \(\sqrt {99} \)= 9.9487… to the exact number d = 0.06.
b) Round b = 7 891 233 to precision d = 50
Solution method
Rounding to the exact number d is that we need to round to the number of parts by d . For example d = 0.06 then we need to round to tenths.
Detailed explanation
a) With an exact number d = 0.06, the number a needs to be rounded to tenths.
Rounded row digit is 9, the digit immediately after the rounded row is 4 < 5, so we keep the rounded row digit, the decimal places after the rounding row are removed, we get:
a = \(\sqrt {99}\) = 9.9487… ≈ 9.9.
b) With the exact number d = 50, the number b needs to be rounded to the hundredth.
The rounded row digit is 2, the number immediately after the rounded row is 3 < 5, so we keep the rounded row digit, the digits after the rounded row are replaced with zero, we get:
b = 7 891 233 7 891 200
Solve problem 5 pages 45 SBT Math 7 Creative horizon episode 1
Use a calculator to calculate and then round the following numbers to the nearest thousandth: \( – 44\sqrt 2 \);\(\pi \sqrt {10} \);\(\sqrt 8 \);\( – \sqrt 2 \)
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Solution method
We use a calculator to calculate the above numbers and then convert them to decimals and round them to the thousandths.
Detailed explanation
Using a calculator, we get: \( – 44\sqrt 2 \) = – 62,22539674…
The rounded row digit is 5, the number after the rounded row is 3 < 5, so keep the rounded row digit, the decimal digits after the rounding row are removed, we get:
\( – 44\sqrt 2 \)= –62,22539674… ≈ – 62.225.
Using a calculator, we get: \(\pi \sqrt {10} \) = 9,934588266…
The rounded digit is 4, the digit after the rounded row is 5 = 5, so we add to the row digit to round 1 unit, the decimal digits after the rounding row are omitted, we get:
\(\pi \sqrt {10} \) = 9,934588266… ≈ 9,935.
Using a calculator, we get: \(\sqrt 8 \) = 2.828427125…
Rounded row digit is 8, the number after the rounding row is 4 < 5, so keep the rounded row digit, the decimal places after the rounding row are removed, we get:
\(\sqrt 8 \) = 2.828427125… ≈ 2.828.
Using a calculator, we get: \( – \sqrt 2 \) = – 1.414213562…
The rounded row digit is 4, the number after the rounded row is 2 < 5, so keep the rounded row digit, the decimal digits after the rounding row are removed, we get:
–1.414213562… ≈ – 1.414
Solve lesson 6 page 45 SBT Math 7 Creative horizon episode 1
The population of Japan as of July 18, 2021 is 126 028 965 people. Please round this number to the thousands.
Solution method
To round decimals to a certain rounding row:
Step 1: Underline the decimal place of the rounded row.
Step 2: Look at the digit immediately to the right
+ If the digit is greater than or equal to 5, increase the underscore by 1 and then replace all the digits to the right with 0 or omit them if they are in decimal.
+ If the digit is less than 5, keep the dashed digit and replace all the digits to the right with 0 or omit it if they are in the decimal part.
Detailed explanation
The rounded row digit is 8, the number after the rounded row is 9 > 5, so we add 1 unit of the rounded row digit, the digits after the rounded row are replaced with zero, we get:
126 028 965 ≈ 126 029 000.
So 126 028 965 ≈ 126 029 000.
Solve problem 7 page 45 SBT Math 7 Creative horizon episode 1
Say 1 inch = 2.54 cm. Calculate the length of the screen diagonal of 65 inches in centimeters and round to units.
Solution method
We calculate how many centimeters is 65 inches, then we will get the number of centimeters that need to be rounded to units.
Detailed explanation
We have 65 inches = 165.1 cm.
The rounded row digit is 5, the number after the rounded row is 1 < 5, so we keep the rounded row digit, the digits after the rounded row are replaced with zero, we get:
165.1 ≈ 165.
So the length of the screen diagonal of 65 inches in cm and rounded to the unit is 165 cm
Solve problem 8 page 45 SBT Math 7 Creative horizon episode 1
Calculate the perimeter and area of a circle with radius 55.24 cm and round to the nearest hundredth.
Solution method
We use the definition of the square root and the formula for the circumference and area of a circle to find the radius
Detailed explanation
Perimeter of a given circle is:
2.π.R = 2.π.55.24 = 347.0831564… ≈ 347.08 (cm).
The area of a given circle is:
.R2 = .55.242 = 9586,436779… ≈ 9586.44 (cm2).
So the perimeter and area of a circle with radius 55.24 cm and rounded to the nearest hundredth is 347.08 cm respectively.2 and 9586.44 cm2