Detailed Calculation Examples of Rounding calculator

Example 1: Rounding a Decimal (Using Predefined Option)

Problem: Round 123.4567 to the nearest hundredth.

Calculator’s Step-by-Step Process:

1. Interpret the Request: “Round to the nearest hundredth” means we need 2 digits after the decimal point.
2. Identify the Target Digit: The hundredths place is the second digit after the decimal. In 123.45**6**7, the target digit is 5.
3. Identify the Decider Digit: This is the digit immediately to the right of the target digit, which is 6 (the thousandths place).
4. Apply the Rounding Rule: Is the decider digit 6 ≥ 5? Yes, it is.
5. Perform the Action: Therefore, we must round the target digit up from 5 to 6. The digits to the right of the target digit become zero (or are dropped after the decimal).
   • Original: 123.4567
   • After rounding up the hundredths place: 123.4667
   • Truncate after the hundredths place: 123.46
6. Final Result: 123.46

Example 2: Rounding a Large Number (Using Custom Precision)

Problem: Round 78,951 to the nearest hundred.

Calculator’s Step-by-Step Process:

1. Interpret the Request: “Nearest hundred” means we want our number to end with the last two digits being 00. The hundreds place is the third digit from the right.
2. Identify the Target Digit: In 78,9**5**1, the hundreds place is occupied by 9.
3. Identify the Decider Digit: This is the digit to the right of the target digit, which is 5 (the tens place).
4. Apply the Rounding Rule: Is the decider digit 5 ≥ 5? Yes, it is.
5. Perform the Action: We round the target digit 9 up. Since 9 becomes 10, it causes a cascade (carry-over).
   • The 9 in the hundreds place becomes 0, and we add 1 to the thousands place.
   • The thousands place is 8, which becomes 9.
   • The final number becomes 79,000.
6. Final Result: 79,000

Example 3: Advanced/Custom Rounding

Problem: Round 17.83 to the nearest 0.25.

Calculator’s Step-by-Step Process:

1. Interpret the Request: Rounding to the nearest 0.25 is equivalent to rounding to the nearest quarter. The calculator likely does this by dividing the number by the precision unit, rounding that result to the nearest whole number, and then multiplying back.
2. Step 1 – Divide: 17.83 / 0.25 = 71.32
3. Step 2 – Round to Whole Number: Round 71.32 to the nearest whole number.
   • Target Digit: 1 (ones place)
   • Decider Digit: 3 (tenths place)
   • Is 3 ≥ 5? No. So, we round down.
   • Result: 71
4. Step 3 – Multiply Back: 71 * 0.25 = 17.75
5. Final Result: 17.75

Example 4: Rounding a Negative Number

Problem: Round -4.7 to the nearest whole number.

Calculator’s Step-by-Step Process:

1. Interpret the Request: The rules of rounding apply the same way to the absolute value of the number, and the sign is preserved.
2. Identify the Target Digit: The whole number part is 4.
3. Identify the Decider Digit: The digit immediately to the right (the tenths place) is 7.
4. Apply the Rounding Rule: Is 7 ≥ 5? Yes, it is.
5. Perform the Action: Therefore, we round the absolute value up from 4 to 5.
6. Apply the Sign: The result is -5.
7. Final Result: -5