Question

rounding worksheet
round the following numbers to the accuracy of the underlined digit.
for example, 5678 means you round to the nearest ten.
1 a. 2642
1 b. 6684
2 a. 7191
2 b. 1335
3 a. 1881
3 b. 9388
4 a. 4674
4 b. 6837
5 a. 2347
5 b. 9934
6 a. 4882
6 b. 2327
7 a. 4214
7 b. 9418
8 a. 8806
8 b. 8954
9 a. 7220
9 b. 4122
10 a. 7892
10 b. 8976
11 a. 9465
11 b. 4558

Answer:

To solve these rounding problems, we follow the rule: look at the digit to the right of the underlined digit. If it is 5 or greater, we round up (increase the underlined digit by 1); if it is less than 5, we round down (keep the underlined digit as it is) and set all digits to the right of the underlined digit to 0. Let's solve a few examples (we'll do 1a, 1b, 2a, 2b as samples; the process is similar for others):

1a. \( 2\underline{6}42 \)

Step1: Identify place & next digit

Underlined digit: 6 (hundreds place). Next digit: 4 (tens place, \( 4 < 5 \)).

Step2: Round down

Keep 6, set right digits to 0.
\( 2642 \approx 2600 \)

1b. \( \underline{6}684 \)

Step1: Identify place & next digit

Underlined digit: 6 (thousands place). Next digit: 6 (hundreds place, \( 6 \geq 5 \)).

Step2: Round up

6 + 1 = 7, set right digits to 0.
\( 6684 \approx 7000 \)

2a. \( \underline{7}191 \)

Step1: Identify place & next digit

Underlined digit: 7 (thousands place). Next digit: 1 (hundreds place, \( 1 < 5 \)).

Step2: Round down

Keep 7, set right digits to 0.
\( 7191 \approx 7000 \)

2b. \( \underline{1}335 \)

Step1: Identify place & next digit

Underlined digit: 1 (thousands place). Next digit: 3 (hundreds place, \( 3 < 5 \)).

Step2: Round down

Keep 1, set right digits to 0.
\( 1335 \approx 1000 \)

3a. \( 1\underline{8}81 \)

Step1: Identify place & next digit

Underlined digit: 8 (hundreds place). Next digit: 8 (tens place, \( 8 \geq 5 \)).

Step2: Round up

8 + 1 = 9, set right digits to 0.
\( 1881 \approx 1900 \)

3b. \( \underline{9}388 \)

Step1: Identify place & next digit

Underlined digit: 9 (thousands place). Next digit: 3 (hundreds place, \( 3 < 5 \))? Wait, no—wait, 9388: underlined is 9 (thousands). Next digit is 3 (hundreds, \( 3 < 5 \))? Wait, no, 9388: thousands digit is 9, next digit (hundreds) is 3. But wait, 9388 rounded to thousands place: since 3 < 5, we keep 9, set right to 0? Wait, no—wait, 9388: thousands place is 9, hundreds digit is 3. So 9388 ≈ 9000? Wait, no, wait: 9388, underlined is 9 (thousands). Next digit is 3 (hundreds). Since 3 < 5, we round down: 9000. Wait, but let's check again. Wait, 9388: thousands digit 9, hundreds 3. So yes, 9388 ≈ 9000.

4a. \( 4\underline{6}74 \)

Step1: Identify place & next digit

Underlined digit: 6 (hundreds place). Next digit: 7 (tens place, \( 7 \geq 5 \)).

Step2: Round up

6 + 1 = 7, set right digits to 0.
\( 4674 \approx 4700 \)

4b. \( 68\underline{3}7 \)

Step1: Identify place & next digit

Underlined digit: 3 (tens place). Next digit: 7 (ones place, \( 7 \geq 5 \))? Wait, no—wait, 6837: underlined is 3 (tens). Next digit is 7 (ones, \( 7 \geq 5 \)). So round up: 3 + 1 = 4, set ones to 0.
\( 6837 \approx 6840 \)

5a. \( \underline{2}347 \)

Step1: Identify place & next digit

Underlined digit: 2 (thousands place). Next digit: 3 (hundreds place, \( 3 < 5 \)).

Step2: Round down

Keep 2, set right digits to 0.
\( 2347 \approx 2000 \)

5b. \( 99\underline{3}4 \)

Step1: Identify place & next digit

Underlined digit: 3 (tens place). Next digit: 4 (ones place, \( 4 < 5 \)).

Step2: Round down

Keep 3, set ones to 0.
\( 9934 \approx 9930 \)

6a. \( 4\underline{8}82 \)

Step1: Identify place & next digit

Underlined digit: 8 (hundreds place). Next digit: 8 (tens place, \( 8 \geq 5 \)).

Step2: Round up

8 + 1 = 9, set right digits to 0.
\( 4882 \approx 4900 \)

6b. \( 2\underline{3}27 \)

Step1: Identify place & next digit

Underlined digit: 3 (hundreds place). Next digit: 2 (tens place, \( 2 < 5 \)).

Step2: Round down

Keep 3, set right digits to 0.
\( 2327 \approx 2300 \)

7a. \( 4\underline{2}14 \)

Step1: Identify place & next digit

Underlined digit: 2 (hundreds place). Next digit: 1 (tens place, \( 1 < 5 \)).

Step2: Round down

Keep 2, set right digits to 0.
\( 4214 \approx 4200 \)

7b. \( 9\underline{4}18 \)

Step1: Identify place & next digit

Underlined digit: 4 (hundreds place). Next digit: 1 (tens place, \( 1 < 5 \)).

Step2: Round down

Keep 4, set right digits to 0.
\( 9418 \approx 9400 \)

8a. \( \underline{8}806 \)

Step1: Identify place & next digit

Underlined digit: 8 (thousands place). Next digit: 8 (hundreds place, \( 8 \geq 5 \)).

Step2: Round up

8 + 1 = 9, set right digits to 0.
\( 8806 \approx 9000 \)

8b. \( 8\underline{9}54 \)

Step1: Identify place & next digit

Underlined digit: 9 (hundreds place). Next digit: 5 (tens place, \( 5 \geq 5 \)).

Step2: Round up

9 + 1 = 10, carry over: hundreds digit becomes 0, thousands digit (8) becomes 8 + 1 = 9.
\( 8954 \approx 9000 \) (Wait, no—wait, 8954: underlined is 9 (hundreds). Next digit is 5 (tens). So 9 + 1 = 10, so we carry over to thousands: 8 (thousands) + 1 = 9, hundreds becomes 0, tens/ones 0. So 8954 ≈ 9000? Wait, no—wait, 8954 rounded to hundreds place: 8954. Hundreds digit 9, tens digit 5. So 9 + 1 = 10, so hundreds place becomes 0, thousands place 8 + 1 = 9. So 8954 ≈ 9000.

9a. \( \underline{7}220 \)

Step1: Identify place & next digit

Underlined digit: 7 (thousands place). Next digit: 2 (hundreds place, \( 2 < 5 \)).

Step2: Round down

Keep 7, set right digits to 0.
\( 7220 \approx 7000 \)

9b. \( 4\underline{1}22 \)

Step1: Identify place & next digit

Underlined digit: 1 (hundreds place). Next digit: 2 (tens place, \( 2 < 5 \)).

Step2: Round down

Keep 1, set right digits to 0.
\( 4122 \approx 4100 \)

10a. \( 78\underline{9}2 \)

Step1: Identify place & next digit

Underlined digit: 9 (tens place). Next digit: 2 (ones place, \( 2 < 5 \))? Wait, no—wait, 7892: underlined is 9 (tens). Next digit is 2 (ones, \( 2 < 5 \))? Wait, no, 9 is in tens place, next digit is 2 (ones). Wait, no—wait, 7892: tens digit 9, ones digit 2. Since 2 < 5, we round down? Wait, no—wait, 9 is in tens place. Wait, 7892 rounded to tens place: look at ones digit (2). Since 2 < 5, we keep 9, set ones to 0. So 7892 ≈ 7890? Wait, no—wait, 7892: underlined is 9 (tens). Next digit is 2 (ones). So 9 remains, ones becomes 0. So 7892 ≈ 7890.

10b. \( 89\underline{7}6 \)

Step1: Identify place & next digit

Underlined digit: 7 (tens place). Next digit: 6 (ones place, \( 6 \geq 5 \)).

Step2: Round up

7 + 1 = 8, set ones to 0.
\( 8976 \approx 8980 \)

11a. \( 9\underline{4}65 \)

Step1: Identify place & next digit

Underlined digit: 4 (hundreds place). Next digit: 6 (tens place, \( 6 \geq 5 \)).

Step2: Round up

4 + 1 = 5, set right digits to 0.
\( 9465 \approx 9500 \)

11b. \( 4\underline{5}58 \)

Step1: Identify place & next digit

Underlined digit: 5 (hundreds place). Next digit: 5 (tens place, \( 5 \geq 5 \)).

Step2: Round up

5 + 1 = 6, set right digits to 0.
\( 4558 \approx 4600 \)

Final Answers (Sample for 1a–11b):

1a. \( \boldsymbol{2600} \)
1b. \( \boldsymbol{7000} \)
2a. \( \boldsymbol{7000} \)
2b. \( \boldsymbol{1000} \)
3a. \( \boldsymbol{1900} \)
3b. \( \boldsymbol{9000} \)
4a. \( \boldsymbol{4700} \)
4b. \( \boldsymbol{6840} \)
5a. \( \boldsymbol{2000} \)
5b. \( \boldsymbol{9930} \)
6a. \( \boldsymbol{4900} \)
6b. \( \boldsymbol{2300} \)
7a. \( \boldsymbol{4200} \)
7b. \( \boldsymbol{9400} \)
8a. \( \boldsymbol{9000} \)
8b. \( \boldsymbol{9000} \)
9a. \( \boldsymbol{7000} \)
9b. \( \boldsymbol{4100} \)
10a. \( \boldsymbol{7890} \)
10b. \( \boldsymbol{8980} \)
11a. \( \boldsymbol{9500} \)
11b. \( \boldsymbol{4600} \)