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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:

.R^{2} = .55.24^{2} = 9586,436779… ≈ 9586.44 (cm^{2}).

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 cm^{2 }