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Election 2015: What does a billion pounds actually buy the nation?

Equation: £1bn=?

Billions are the basic unit of general election pledges. But it can be hard to comprehend such vast sums. So what does £1bn of public spending really mean?

Spell it out - £1,000,000,000 - and the nine noughts blur into a statistical mirage. A billion pounds is both utterly familiar and hard to get your head round.

It's a lot of cash. But today politicians regard anything less as loose change.

The Conservatives want to plough £18bn into a new "right to buy" scheme and Labour plans to cut tuition fees at a cost of £2.9bn. UKIP will spend an extra £3bn on defence, while the Lib Dems are promising £3.5bn for mental health services. The Scottish National Party wants Scotland's health budget to rise by £2bn by 2020 while Plaid Cymru calls for an additional £1.2bn for Wales.

Such sums are dizzying. A standard calculator only has room for seven noughts.

Spending in the millions used to get a look-in at elections. The Conservative 1987 manifesto reads: "We have set up a special £50 million two-year programme. This year it will give treatment to over 100,000 people who are waiting for operations." Today all three main parties are pledging increases of between £2.5bn and £8bn for the NHS.

The billion's central role is a result of decades of economic growth and inflation, says Mike Ellicock, chief executive of the charity National Numeracy. "That's the reality when you're looking at more than £700bn public sector spending and GDP of £1.5tn."

So what does £1bn buy the government?

Welfare is one of the biggest spending demands for governments. Depending on your definition, it accounts for a quarter or over a half of government spending.

A billion pounds will buy 147,000 state pensions or 300,000 jobseeker's allowances for a year, according to Department for Work and Pensions forecasts for 2015/16. Alternatively it could fund 2.3 million people's disability living allowance per annum - three quarters of the total.

Health is a huge eater-up of funds. Think tank the King's Fund says that £1bn will pay to run the NHS across the UK for nearly three days. Alternatively it would cover all diagnostic imaging - MRI scans, x-rays - for a year with a bit left over for other jobs. Or another way would be to fund 26,000 nurses or 12,000 hospital doctors for a year.

What about treatment? It could pay for 167,000 hip replacements or 1.4 million hospital day cases. A billion pounds could also pay for two flagship hospitals, such as Birmingham's Queen Elizabeth Hospital which opened in 2010.

Mental health is becoming a bigger election issue. A billion pounds would provide an eight-hour course of talking therapy for 2.5m people. Or 750,000 eight-session courses of mindfulness therapy, based on figures from the Personal Social Services Research Unit.

Military spending, at about £37bn a year, is dwarfed by the NHS's £130bn. But a billion pounds doesn't go far with high-tech kit, says Prof John Louth, a director at defence think tank the Royal United Services Institute.

It could pay for two navy frigates. Or just the engines (known as "power plant") of a nuclear powered submarine. It would buy about a quarter of the new Queen Elizabeth aircraft carrier. Or you could afford three or four F35B aircraft to fly off the carrier. In terms of more conventional fast jets, it could purchase about 10 fully equipped Typhoons. Or the army could pay for 40 Challenger 2 tanks. The basic production cost in 2002 of each tank was £6m. But add in personnel, logistics and maintenance costs over its lifetime and you reach a figure of £25m, Louth estimates.

Turning to manpower, £1bn could fund 8,500 troops. What about combat? Foreign wars are hard to cost. In 2014 Rusi estimated that the cost of UK operations in Iraq between 2003 and 2009 was £9.56bn and more than double that in Afghanistan. All of this is dwarfed by the cost of Trident, which is estimated at between £100bn and £120bn.

Education has a similar budget to defence. With £1bn the government could, for a year, fund 27,000 primary or 22,000 secondary school teachers, says Rebecca Allen, director at Education Datalab, a research centre. Or give free school meals to 2.5m children.

New schools - like hospitals - are hard to cost. The average cost of a free school is £6.6 million - so that would mean about new 150 free schools. These tend to be smaller than conventional schools and the figure includes primaries. Using the last Labour government's Building Schools for the Future programme the average cost of a secondary school was £25m. That would mean an extra 40 secondary schools.

The housing shortage is a long-standing issue. With £1bn the government could build 16,600 new social homes or 50,000 shared ownership homes, according to the charity Shelter.

Or what about transport? Rail expert Christian Wolmar says for that money you could electrify about 125 miles of train lines. Or complete 10 or 15% of the proposed HS3 line linking Manchester and Hull. Spend the money on roads instead and what can you get for £1bn? The government set out plans last year to turn the main route to Southwest England along the A303 and A358 into a dual carriageway with a tunnel at Stonehenge. A billion would pay for half the job.

Think tank the IPPR suggests other things a billion could pay for: 180,000 jobs guaranteed at the minimum wage for 30 hours a week, or support for 100,000 socially excluded families.

What about hard-working families, that oft uttered mantra? The IPPR says £1bn could make universal the offer of 15 hours a week of childcare for 37 weeks of the year. This is currently available to only the 40% most disadvantaged two-year olds.

The permutations for spending and cutting are almost limitless. Voters have to decide which party they trust to make the difficult decisions. But breaking down the big numbers - like the NHS budget - can help people make sense of it all, says Ellicock.

Public spending in the UK surpassed a thousand million many decades ago. But billion was avoided. Discussing the budget of 1953, the Times talks of expenditure "in excess of last year's original estimate of £4,200m".

Back then, a billion meant what schoolchildren until recently called a "British billion" meaning a million million. An American billion was a thousand million. But in the 1970s Prime Minister Harold Wilson shifted the UK public sector onto US terminology, angering traditionalists.

What is a billion?

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"The answer is one thousand million - 1,000,000,000. Historically, however, in the UK the term billion meant a million million - 1,000,000,000,000. It was changed to conform with the US understanding of a billion - which was one thousand million. The US value had become increasingly used in Britain and the Prime Minister, Harold Wilson confirmed in a written reply in 1974 that the meaning of 'billion' would be thousand-million, in accordance with international usage."

House of Commons Library

There are other factors. Is it money to be invested in a single year or every year for the parliament? And is it capital investment - generally investing in infrastructure - or current spending on wages?

Then there's the question of how you say it. Gordon Brown as chancellor had the rather peculiar habit of adding an "s" with figures. So in his 2004 budget he spoke of borrowing in future years being "£37.5 billions, £33 billions, and then £31, £27, £27 and £23 billions".

The Oxford English Dictionary's first record of billion is attributed to philosopher John Locke in 1690. Locke's usage seems more poetic than mathematical: "Nonilions. Octilions... Trilions. Bilions. Milions. Vnites."

A billion doesn't go far these days in the US. In February President Obama proposed a $4 trillion budget. The same goes for discussing Greek bailouts or ordinary people trying to survive in countries with rampant inflation - like Zimbabwe in the past decade. Only a trillion will do.

But for UK elections, the billion holds sway. James Abdey, lecturer in statistics at the LSE, says ordinary people can't really conceptualise a billion. The closest most of us get is understanding that a house might cost one or two million pounds. "Once you go beyond that these are not everyday figures that people can comprehend."

It leaves Ellicock concerned. "There's an interesting question - does the electorate really understand the (vast) difference between a million and a billion?" He offers an example. Ask someone how long a million seconds is - the answer is 12 days. Ask them to think how long a billion seconds is and they may well answer in days. The answer is 32 years.

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