CBSE Class 6 Maths Advanced Knowing Our Numbers MCQs Set 01

Answer: (b) 50,000

Explanation:
1. The successor of a number is the number that is 1 more than it.
2. 49,999 + 1 = 50,000.

Teacher's Note:
1. Successor means add 1; predecessor means subtract 1.
2. Watch the carry when the number ends in 9s.

Answer: (c) 15198

Explanation:
1. All four numbers are 5-digit numbers starting with 15, so compare the hundreds digit.
2. The hundreds digits are 6, 7, 1 and 6; the smallest is 1.
3. So the smallest numeral is 15198.

Teacher's Note:
1. With equal digit counts, compare from the left.
2. Stop at the first place where the digits differ.

Answer: (c) 789499

Explanation:
1. A number 'comes just after' its predecessor.
2. The predecessor of 789500 is 789500 − 1 = 789499.

Teacher's Note:
1. 'Just after' means the number before it is 1 less.
2. Do not confuse it with 'just before'.

Answer: (c) 90000

Explanation:
1. Write the digits with their places: 7 (ten lakh), 6 (lakh), 9 (ten thousand), 0 (thousand), 4 (hundred), 5 (ten), 3 (one), that is 76,90,453.
2. 9 is in the ten-thousands place, so its place value is 90000.

Teacher's Note:
1. Count places from the right: ones, tens, hundreds, thousands, ten thousands.
2. 9 is the fifth digit from the right.

Answer: (b) 7

Explanation:
1. 57,168 has places: 5 (ten thousands), 7 (thousands), 1 (hundreds), 6 (tens), 8 (ones).
2. The digit at thousands place is 7.

Teacher's Note:
1. Make a place-value chart when unsure.
2. The comma in 57,168 separates the thousands period.

Answer: (c) 400000

Explanation:
1. 428721: the first 2 is in the ten-thousands place, so its value is 20000.
2. The second 2 is in the tens place, so its value is 20.
3. Product = 20000 × 20 = 400000.

Teacher's Note:
1. Find each place value separately, then multiply.
2. Count the zeros carefully: 4 zeros + 1 zero + the 2 × 2 = 4.

Answer: (c) 37904

Explanation:
1. 3 × 10000 = 30000; 7 × 1000 = 7000; 9 × 100 = 900; 0 × 10 = 0; and 4.
2. Sum = 30000 + 7000 + 900 + 0 + 4 = 37904.

Teacher's Note:
1. An expanded form is just the digits written in their places.
2. A zero multiplier means the digit 0 in that place.

Answer: (c) 5,86,95,376

Explanation:
1. In the Indian system the first comma comes after 3 digits from the right, then after every 2 digits.
2. 58695376 → 376 | 95 | 86 | 5 gives 5,86,95,376.

Teacher's Note:
1. Indian grouping is 3, then 2, 2, 2.
2. The International system would write 58,695,376 instead.

Answer: (c) 74570

Explanation:
1. Seventy-four thousand = 74000.
2. Five hundred seventy = 570.
3. 74000 + 570 = 74570.

Teacher's Note:
1. Write the thousands part first, then the rest.
2. Check each option's last three digits against 'five hundred seventy'.

Answer: (b) 254321.

Explanation:
1. One crore = 1,00,00,000 = 10000000.
2. Difference = 10000000 − 9745679 = 254321.

Teacher's Note:
1. Convert the crore to digits first.
2. Subtract carefully with borrowing.

Answer: (d) 10000

Explanation:
1. The greatest 4-digit number is 9999.
2. Its successor is 9999 + 1 = 10000.

Teacher's Note:
1. The successor of the greatest n-digit number is the smallest (n+1)-digit number.
2. 10000 is the smallest 5-digit number.

Answer: (a) 9875

Explanation:
1. To make the largest number, put the greatest digit first, then the next greatest and so on.
2. Descending order of the digits: 9, 8, 7, 5, giving 9875.

Teacher's Note:
1. Largest number: digits in descending order.
2. Smallest number: digits in ascending order.

Answer: (c) 2059

Explanation:
1. The smallest arrangement is 0, 2, 5, 9 but 0 cannot be the first digit of a 4-digit number.
2. So put 2 first, then 0, 5, 9: 2059.

Teacher's Note:
1. 0295 is only a 3-digit number, 295.
2. Place the smallest non-zero digit first.

Answer: (d) 9965

Explanation:
1. For the largest number we repeat the greatest digit, 9.
2. Digits to use: 9, 9, 6, 5 (the next greatest after 9 are 6 and 5).
3. Arranged in descending order: 9965.

Teacher's Note:
1. Repeat the greatest digit for the largest number.
2. Repeat the smallest digit for the smallest number.

Answer: (a) 49500

Explanation:
1. In 57568 the first 5 is at the ten-thousands place: 50000.
2. The second 5 is at the hundreds place: 500.
3. Difference = 50000 − 500 = 49500.

Teacher's Note:
1. Both 5s have the same face value but different place values.
2. Subtract the smaller place value from the larger.

Answer: (d) 50

Explanation:
1. 37 × 23 = 851.
2. The digits are 8, 5 and 1. Only 5 is a prime number (8 is composite and 1 is not prime).
3. 5 is in the tens place, so its place value is 50.

Teacher's Note:
1. Prime numbers have exactly two factors; 1 is not prime.
2. First find the product, then look at each digit.

Answer: (b) 991000

Explanation:
1. 1 million = 1000000.
2. 900 tens = 900 × 10 = 9000.
3. Difference = 1000000 − 9000 = 991000.

Teacher's Note:
1. Change 'tens' to a number by multiplying by 10.
2. 1 million has six zeros.

Answer: (c) 999950

Explanation:
1. 1 million = 1000000.
2. 50 less than it = 1000000 − 50 = 999950.

Teacher's Note:
1. 'Less than' means subtract.
2. Subtracting 50 from the zeros of 1000000 changes only the last two places.

Answer: (d) 4

Explanation:
1. A 3-digit number cannot start with 0.
2. With 1 first: 102, 120. With 2 first: 201, 210.
3. Total = 4 numbers.

Teacher's Note:
1. List the numbers systematically by the first digit.
2. Do not count numbers that start with 0.

Answer: (d) 6

Explanation:
1. An odd number must end in an odd digit. The only odd digit available is 1, so 1 must be in the ones place.
2. The other three digits 4, 6, 8 can be arranged in 3 × 2 × 1 = 6 ways.
3. So 6 odd numbers can be formed.

Teacher's Note:
1. The last digit decides odd or even.
2. Fix the ones digit first, then arrange the rest.

Answer: (d) 86000

Explanation:
1. Look at the hundreds digit, which is 6.
2. 6 is 5 or more, so the thousands digit 5 goes up to 6 and the lower digits become 0.
3. 85642 rounds to 86000.

Teacher's Note:
1. Rounding to thousands: look at the hundreds digit.
2. 5 or more rounds up, less than 5 rounds down.

Answer: (d) 5499

Explanation:
1. Numbers from 4500 to 5499 round to 5000 (nearest thousand).
2. 5500 and above round up to 6000.
3. The greatest such number is 5499.

Teacher's Note:
1. The limit is where the hundreds digit is 4.
2. The smallest number that rounds up to 5000 is 4500.

Answer: (c) 5090

Explanation:
1. 439 ≈ 440, 334 ≈ 330 and 4317 ≈ 4320.
2. Sum ≈ 440 + 330 + 4320 = 5090.

Teacher's Note:
1. Round each number first, then add.
2. Look at the ones digit to round to tens.

Answer: (b) 495213

Explanation:
1. Numbers from 495000 to 504999 round to 500000 (nearest ten thousand).
2. 492811 rounds to 490000, 589200 to 590000 and 513076 to 510000.
3. Only 495213 rounds to 500000.

Teacher's Note:
1. Look at the thousands digit when rounding to ten thousands.
2. Round each option and compare.

Answer: (c) 5660 × 2230

Explanation:
1. The best estimate is the one closest to the actual numbers.
2. 5663 ≈ 5660 and 2234 ≈ 2230 (rounded to the nearest ten) are the closest roundings.
3. So the best estimation is 5660 × 2230.

Teacher's Note:
1. Rounding to a smaller place gives a more exact estimate.
2. Compare how far each rounded number is from the original.

Answer: (b) 100

Explanation:
1. A quintal is a unit of weight equal to 100 kilograms.
2. So 1 quintal = 100 kg.

Teacher's Note:
1. 1 tonne = 10 quintals = 1000 kg.
2. Learn the common units of weight together.

Answer: (c) 200103 cm

Explanation:
1. Change everything to cm: 1 km = 1000 m = 100000 cm, so 2 km = 200000 cm.
2. 1 m = 100 cm and 3 cm stays 3 cm.
3. Total = 200000 + 100 + 3 = 200103 cm.

Teacher's Note:
1. Convert all quantities to the same unit before adding.
2. 1 km = 100000 cm.

Answer: (b) 2

Explanation:
1. One dozen means 12.
2. Cost of 1 banana = 24 ÷ 12 = Rs. 2.

Teacher's Note:
1. A dozen is 12 items.
2. Use division to find the cost of one.

Answer: (c) 1620

Explanation:
1. Distance = speed × time = 45 × 36.
2. 45 × 36 = 1620.
3. The train covers 1620 km.

Teacher's Note:
1. Distance = speed × time.
2. Check: 45 × 36 = 45 × 30 + 45 × 6 = 1350 + 270.

Answer: (c) 252Kg 630g

Explanation:
1. 14 kg × 18 = 252 kg.
2. 35 g × 18 = 630 g.
3. Total = 252 kg 630 g.

Teacher's Note:
1. Multiply the kg part and the g part separately.
2. If the grams cross 1000, convert them to kg.

Answer: (c) 65

Explanation:
1. L = 50, X = 10 and V = 5, all in descending order, so they are added.
2. 50 + 10 + 5 = 65.

Teacher's Note:
1. Add when a smaller symbol follows a larger one.
2. Read from left to right.

Answer: (b) 999

Explanation:
1. CM = 1000 − 100 = 900.
2. XC = 100 − 10 = 90.
3. IX = 10 − 1 = 9.
4. Total = 900 + 90 + 9 = 999.

Teacher's Note:
1. Break a Roman numeral into groups such as CM, XC, IX.
2. Each subtractive pair is a single value.

Answer: (d) VII

Explanation:
1. IV = 4, V = 5, VI = 6, VII = 7.
2. The greatest is VII.

Teacher's Note:
1. Convert each numeral first.
2. IV is less than V because I is subtracted.

Answer: (d) VXXX

Explanation:
1. VIII = 8, XX = 20 and XVI = 16 are all valid.
2. In VXXX the symbol V is written before the larger symbol X, but V can never be subtracted, so VXXX is meaningless.

Teacher's Note:
1. V, L and D are never subtracted.
2. Check the rules for each symbol.

Answer: (d) LLX

Explanation:
1. LXXX = 80, LXX = 70 and LX = 60 are correct.
2. In LLX the symbol L is repeated, but V, L and D can never be repeated, so LLX is incorrect.

Teacher's Note:
1. V, L and D are never repeated.
2. Only I, X, C and M can repeat, up to three times.

Answer: (d) 1 crore

Explanation:
1. The greatest 7-digit number is 9999999.
2. 9999999 + 1 = 10000000 = 1 crore.

Teacher's Note:
1. Adding 1 to the greatest n-digit number gives the smallest (n+1)-digit number.
2. 10000000 is written 1,00,00,000 in the Indian system.

Answer: (c) 6034579

Explanation:
1. 6 stays in the first place. The other digits are 3, 5, 0, 9, 4, 7.
2. Arrange them in ascending order: 0, 3, 4, 5, 7, 9.
3. The number is 6034579.

Teacher's Note:
1. Smallest number: ascending order of the other digits.
2. Here 0 may be used because 6 already leads the number.

Answer: (d) 18,000

Explanation:
1. The digits are 1, 0, 2, 3, 5, 0, 0, 7.
2. Largest number: 75321000, where 2 is in the ten-thousands place, so its place value is 20000.
3. Smallest number: 10002357 (0 cannot be first), where 2 is in the thousands place, so its place value is 2000.
4. Difference = 20000 − 2000 = 18000.

Teacher's Note:
1. Write the largest and smallest numbers first.
2. A number cannot start with 0.

Answer: (d) 9965

Explanation:
1. Repeat the greatest digit 9 and use the next greatest digits 6 and 5.
2. In descending order the number is 9965.

Teacher's Note:
1. For the largest number repeat the greatest digit.
2. Then arrange all digits from the greatest to the smallest.

Answer: (a) 99987

Explanation:
1. Use the greatest digit 9 as many times as possible, and the next two greatest digits 8 and 7 once each.
2. The digits 9, 9, 9, 8, 7 in descending order give 99987.

Teacher's Note:
1. Exactly three different digits are needed.
2. Repeat 9 to keep the number as large as possible.