R d sharma mathematics solutions class 6 Solutions for Chapter 1 knowing your numbers

Write each of the following in expanded notation:

(i) 3057

(ii) 12345

(iii) 10205

(iv) 235060

Write the corresponding numeral for each of the following:

(i) 7 × 1000 + 2 × 1000 + 5 × 100 + 9 × 10 + 6 × 1

(ii) 4 × 100000 + 5 × 1000 + 1 × 100 + 7 × 1

(iii) 8 × 1000000 + 3 × 1000 + 6 × 1

(iv) 5 × 10000000 + 7 × 1000000 + 8 × 1000 + 9 × 10 + 4

Find the place value of the digit 4 in each of the following:

(i) 74983160

(ii) 8745836

Determine the product of the place values of two fives in 450758.

Determine the difference of the place values of two 7’s in 257839705.

Determine the difference between the place value and the face value of 5 in 78654321.

Which digits have the same face value and place value in 92078634?

How many different 3-digit numbers can be formed by using the digits 0, 2, 5 without repeating any digit in the number?

Write all possible 3-digit numbers using the digits 6, 0, 4 when

(i) repetition of digits is not allowed

(ii) repetition of digits is allowed.

Fill in the blank:

(i) 1 lakh = …………. Ten thousand

(ii) 1 lakh = ………… Thousand

(iii) 1 lakh = ………….Hundred

(iv) 1 lakh = …………. ten

(v) 1 crore = …………..ten lakh

(vi) 1 crore = ………….lakh

(vii) 1 crore =…………Ten thousand

(viii) 1 crore = ………..thousand

(ix) 1 crore = ……………Hundred

(x) 1 crore = ………………Ten

Write the roman-numerals for each of the following:

(i) 33

(ii) 48

(iii) 76

(iv) 95

Write the following in Roman numerals:

(i) 154

(ii) 173

(iii) 248

(iv) 319

Write the following in Roman numerals:

(i) 1008

(ii) 2718

(iii) 3906

(iv) 3794

Write each of the following numbers in digits by using international place value chart. Also, write them in expanded form

(i) Seven million three hundred three thousand two hundred six.

(ii) Fifty five million twenty nine thousand seven.

(iii) Six billion one hundred ten million three thousand seven.

How many four digit numbers are there in all?

Rewrite each of the following numerals with proper commas in the international system of numeration. Also, write the number name of each in the international system of numeration

(i) 513625

(ii) 4035672

(iii) 65954923

(iv) 70902005

Write each of the following numbers in the International system of numeration:

(i) Forty three lakh four thousand eighty four.

(ii) Six crore thirty four lakh four thousand forty four.

(iii) Seven lakh thirty five thousand eight hundred ninety nine only.

Write the following numbers in the Indian system of numeration:

(i) Six million five hundred forty three thousand two hundred ten.

(ii) Seventy six million eighty five thousand nine hundred eighty seven.

(iii) Three hundred twenty five million four hundred seventy nine thousand eight hundred thirty eight.

A certain nine digit number has only ones in ones period, only twos in the thousands period andonly threes in millions period. Write this number in words in the Indian system.

How many thousands make a million?

How many millions make a billion?

(i) How many lakhs make a million?

(ii) How many lakhs make a billion?

Write each of the following in numeral form:

(i) Eight million seven hundred eight thousand four.

(ii) Six hundred seven million twelve thousand eighty four.

(iii) Four billion twenty five million forty five thousand.

Write the number names of each of the following in international system of numeration:

(i) 435, 002

(ii) 1, 047, 509

(iii) 59, 064, 523

(iv) 25, 201, 905

Write the smallest and the largest six digit numbers. How many numbers are between these two.

How many 8-digit numbers are there in all?

Write 10075302 in words and rearrange the digits to get the smallest and the largest numbers.

What is the smallest 3-digit number with unique digits?

What is the largest 5-digit number with unique digits?

Write the smallest 3-digit number which does not change if the digits are in reverse order.

Find the difference between the number 279 and that obtained on reversing its digits.

Form the largest and smallest 4-digit numbers using each of digits 7, 1, 0, 5 only once

Put the appropriate symbol (<, >) in each of the following boxes:

(i) 102394 ☐ 99887

(ii) 2507324 ☐ 2517324

(iii) 3572014 ☐ 10253104

(iv) 47983505 ☐ 47894012

Arrange the following numbers in ascending order:

(i) 102345694, 8354208, 6539542, 63547201, 12345678

(ii) 1808090, 188088, 181888, 190909, 16060666.

Arrange the following numbers in descending order:

(i) 56943300, 56943201, 5695440, 56944000, 5694437

(ii) 1020216, 1020308, 1021430, 893245, 893425.

How many milligrams make one kilogram?

A box of medicine tablets contains 2, 00, 000 tablets each weighing 20mg. What is the total weight ofall the tablets in the box in grams? In kilograms?

Population of Sundarnagar was 2, 35, 471 in the year 1991. In the year 2001 it was found tohave increased by 72, 958. What was the population of the city in 2001?

A book exhibition was held for four days in a school. The number of tickets sold at the counter on the first, second, third and final days were respectively 1094, 1812, 2050 and 2751. Find the total number of tickets sold on all the four days.

The town newspaper is published everyday. One copy has 12 pages. Everyday 11,980 copies areprinted. How many pages are in all printed everyday? Every month?

A machine, on an average, manufactures 2825 screws a day. How many screws did it produce inthe month of January 2006?

A famous cricket player has so far scored 6978 runs in test matches. He wishes to complete 10, 000 runs.

How many more runs does he need?

Ravish has ₹ 78, 592 with him. He placed an order for purchasing 39 radio sets at ₹ 1234 each. How much money will remain with him after the purchase?

In an election, the successful candidate registered 5, 77, 570 votes and his nearest rival secured 3, 48, 685 votes. By what margin did the successful candidate win the election?

To stitch a shirt 2m 15cm cloth is needed. Out of 40m cloth, how many shirts can be stitched andhow much cloth will remain?

A vessel has 4 litre and 650ml of curd. In how many glasses, each of 25ml capacity, can itbe distributed?

Medicine is packed in boxes, each such box weighing 4kg 500g. How many such boxes can be loadedin a van which cannot carry beyond 800kg?

The distance between the school and the house of a student is 1km 875m.

Everyday she walks both ways between her school and home. Find the total distance covered by her in a week.

Round off each of the following numbers to nearest tens:

(i) 84

(ii) 98

(iii) 984

(iv) 808

(v) 998

(vi) 12, 096

(vii) 10, 908

(viii) 28, 925

Round off each of the following numbers to nearest hundreds:

(i) 3, 985

(ii) 7, 289

(iii) 8, 074

(iv) 14, 627

(v) 28, 826

(vi) 4, 20, 387

(vii) 43, 68, 973

(viii) 7, 42, 898

Round off each of the following numbers to nearestthousands:

(i) 2, 401

(ii) 9, 600

(iii) 4, 278

(iv) 7, 832

(v) 9, 567

(vi) 26, 019

(vii) 20, 963

(viii) 4, 36, 952

Round off each of the following to the nearest tens, hundreds and thousands:

(i) 964

(ii) 1, 049

(iii) 45, 634

(iv) 79, 085

Round off the following measures to the nearest hundreds:

(i) Rs 666

(ii) Rs 850

(iii) Rs 3, 428

(iv) Rs 9, 080

(v) 1, 265 km

(vi) 417m

(vii) 550cm

(viii) 2, 486m

(ix) 360gm

(x) 940kg

(xi) 273l

(xii) 820mg

List all numbers which are rounded off to nearest ten as 370.

Find the smallest and greatest numbers which are rounded off to the nearest hundreds as 900.

Find the smallest and greatest numbers which are rounded off to the nearest thousands as 9000.

Estimate the following by rounding off each factor to nearest hundreds:

(i) 730 + 998

(ii) 796 – 314

(iii) 875 – 384

Estimate the following by rounding off each factor to nearestthousands:

(i) 12, 094 + 2, 888

(ii) 28, 292 – 21, 496

Estimate the following by rounding off each number to its greatest place:

(i) 439 + 334 + 4, 317

(ii) 8, 325 – 491

(iii) 1, 08, 734 – 47, 599

(iv) 898 × 785

(v) 9 × 795

(vi) 87 × 317

Find the estimated quotient for each of the following by rounding off each number to its greatestplace:

(i) 878 ÷ 28

(ii) 745 ÷ 24

(iii) 4489 ÷ 394

Write the expression for each of the following statements using brackets:

(i) Four multiplied by the sum of 13 and 7.

(ii) Eight multiplied by the difference of four from nine.

(iii) Divide the difference of twenty eight and seven by 3.

(iv) The sum of 3 and 7 is multiplied by the difference of twelve and eight

Simplify each of the following:

(i) 124 – (12 – 2) × 9

(ii) (13 + 7) × (9 – 4) – 18

(iii) 210 – (14 – 4) × (18 + 2) – 10

Simplify each of the following:

1. 7 × 109
2. 6 × 112
3. 9 × 105
4. 17 × 109
5. 16 × 108
6. 12 × 105
7. 102 × 103
8. 101 × 105
9. 109 × 107