Round off the following numbers to the nearest hundred, two decimal places, and three significant figures.

Question

ScanSolve AI Tutor · Accepted Answer

Section A: Rounding Off Quantities 1. Round off the following numbers to the nearest hundred: a) 4,372 Step 1: Identify the hundreds digit, which is 3. Step 2: Look at the digit to its right, which is 7. Step 3: Since 7 is 5 or greater, round up the hundreds digit (3 becomes 4). Step 4: Replace the digits to the right with zeros. 4,372 ≈ 4,400 b) 8,950 Step 1: Identify the hundreds digit, which is 9. Step 2: Look at the digit to its right, which is 5. Step 3: Since 5 is 5 or greater, round up the hundreds digit (9 becomes 10, so the thousands digit also increases). Step 4: Replace the digits to the right with zeros. 8,950 ≈ 9,000 2. Round off the following to two decimal places: a) 12.4572 Step 1: Identify the second decimal place, which is 5. Step 2: Look at the digit to its right, which is 7. Step 3: Since 7 is 5 or greater, round up the second decimal place (5 becomes 6). Step 4: Truncate the number after the second decimal place. 12.4572 ≈ 12.46 b) 0.0839 Step 1: Identify the second decimal place, which is 8. Step 2: Look at the digit to its right, which is 3. Step 3: Since 3 is less than 5, keep the second decimal place as it is. Step 4: Truncate the number after the second decimal place. 0.0839 ≈ 0.08 3. Round off the following to three significant figures: a) 56,721 Step 1: Identify the first three significant figures: 5, 6, 7. Step 2: Look at the digit immediately after the third significant figure (7), which is 2. Step 3: Since 2 is less than 5, keep the third significant figure as it is. Step 4: Replace the remaining digits with zeros to maintain the magnitude. 56,721 ≈ 56,700 b) 0.004026 Step 1: Identify the first three significant figures. The leading zeros are not significant. The first significant figure is 4, the second is 0, the third is 2. Step 2: Look at the digit immediately after the third significant figure (2), which is 6. Step 3: Since 6 is 5 or greater, round up the third significant figure (2 becomes 3). Step 4: Truncate the number after the third significant figure. 0.004026 ≈ 0.00403 4. A bag of rice weighs 25.48 kg. Round this weight to the nearest whole number. Step 1: Identify the whole number part, which is 25. Step 2: Look at the digit immediately after the decimal point, which is 4. Step 3: Since 4 is less than 5, keep the whole number as it is. Step 4: Remove the decimal part. 25.48 kg ≈ 25 kg Section B: Estimating Percentages of Quantities 5. Estimate the value of 11% of 198. Show your rounding. Step 1: Round 11% to the nearest 10%, which is 10%. Step 2: Round 198 to the nearest hundred, which is 200. Step 3: Calculate 10% of 200. 10% of 200 = 10/100 × 200 = 0.10 × 200 = 20 6. Estimate the value of 24% of 405. Step 1: Round 24% to the nearest 10% or a common fraction equivalent. 24% is close to 25%. Step 2: Round 405 to the nearest hundred, which is 400. Step 3: Calculate 25% of 400. 25% of 400 = 25/100 × 400 = 1/4 × 400 = 100

Round off the following numbers to the nearest hundred, two decimal places, and three significant figures.

Step-by-step solution

Identify the hundreds digit, which is 3.

Look at the digit to its right, which is 7.

Since 7 is 5 or greater, round up the hundreds digit (3 becomes 4).

Replace the digits to the right with zeros.

Identify the hundreds digit, which is 9.

Look at the digit to its right, which is 5.

Since 5 is 5 or greater, round up the hundreds digit (9 becomes 10, so the thousands digit also increases).

Replace the digits to the right with zeros.

Identify the second decimal place, which is 5.

Look at the digit to its right, which is 7.

Since 7 is 5 or greater, round up the second decimal place (5 becomes 6).

Truncate the number after the second decimal place.

Identify the second decimal place, which is 8.

Look at the digit to its right, which is 3.

Since 3 is less than 5, keep the second decimal place as it is.

Truncate the number after the second decimal place.

Identify the first three significant figures

Look at the digit immediately after the third significant figure (7), which is 2.

Since 2 is less than 5, keep the third significant figure as it is.

Replace the remaining digits with zeros to maintain the magnitude.

Identify the first three significant figures.

Look at the digit immediately after the third significant figure (2), which is 6.

Since 6 is 5 or greater, round up the third significant figure (2 becomes 3).

Truncate the number after the third significant figure.

Identify the whole number part, which is 25.

Look at the digit immediately after the decimal point, which is 4.

Since 4 is less than 5, keep the whole number as it is.

Remove the decimal part.

Round 11% to the nearest 10%, which is 10%.

Round 198 to the nearest hundred, which is 200.

Calculate 10% of 200.

Round 24% to the nearest 10% or a common fraction equivalent.

Round 405 to the nearest hundred, which is 400.

Calculate 25% of 400.

Still stuck on this one?

More Mathematics Questions